Mr McDonnell acknowledged the quality of the shadow foreign secretary’s address, but warned: “It reminded me of Tony Blair’s speech taking us into the Iraq War. I am always anxious that the greatest oratory can lead us into the greatest mistakes.”
Meanwhile, a shadow cabinet minister called on leader Jeremy Corbyn to show “no tolerance” of bullying abuse, as MPs complained of intimidating emails and tweets calling for their deselection.
Shadow home secretary Andy Burnham called for a party code of conduct on the use of social media, and branded Mr Corbyn’s close ally Ken Livingstone “disgraceful” for suggesting that he would back efforts to deselect some of the 66 Labour MPs - including seven shadow cabinet members - who backed air strikes in Wednesday’s free vote.
Labour’s shadow leader in the Commons Chris Bryant called for a security review of MPs’ homes and offices. “Several” MPs’ offices had been barricaded by protesters and one had her house surrounded, while others had been sent photos of dead babies and severed heads, he told the Commons.
Labour MP Wes Streeting - who voted against air strikes - said Mr Corbyn was not “showing strong enough leadership” over what he said had been “a well-organised, systematic, well-resourced attempt to bully Labour MPs into voting against air strikes in Syria”.
And Stockport MP Ann Coffey, who received emails branding her a “warmonger” and a “red Tory”, said that “unfortunate” comments from senior party figures had effectively given campaigners “permission to target MPs”.
Walthamstow MP Stella Creasy, who has faced threats of deselection, was forced to leave the chamber during Syria debate to deal with abusive phone calls to her office.
As far-left political party Left Unity published a list of those who voted for air strikes under the banner “deselect them now”, Mr Livingstone suggested that he would back efforts to remove pro-war MPs.
The former London mayor, who is co-chairing a review of Labour defence policy, told LBC: “If I had an MP who had voted to bomb Syria then I would be prepared to support someone to challenge him.”
Mr Burnham responded: “I think that’s a disgraceful thing to say on a day like today, because we had a free vote in Parliament - there wasn’t a party line. To say they should be subjected to a witch-hunt or a campaign against them is wrong.”
He told BBC2’s Victoria Derbyshire Show: “It makes me sad about the current state of the Labour Party .... A firm line needs to be taken, a code of conduct around social media.
“If there’s evidence that people are abusive of colleagues in the Labour Party there should be no tolerance of that in my view.”
Mr Livingstone later defended his comments, telling the BBC: “Nobody should be doing abusive tweets or anything like that, but people voicing their genuine belief that they would rather have an MP who supports the leader rather than undermines him should be free to say that.”
Mr McDonnell said any complaints would be investigated and members using “unacceptable” bullying or abuse on either side of the debate would face disciplinary action.
Revealing that he had received a death threat for his anti-war stance, the shadow chancellor said: “All of that intimidation is not acceptable. It is not part of the Labour Party.
“If you joined the Labour Party and use that sort of language on either side of the argument, you shouldn’t be in the party. It is unacceptable. Jeremy Corbyn has made that position very, very clear. If they are Labour Party members, we have disciplinary processes and they will take place.”
On Ms Creasy, the shadow chancellor said: “There is no way she should be deselected. She is an excellent MP and she has my support.”
Mr McDonnell dismissed a suggestion from veteran Labour backbencher Frank Field that the party should have two leaders, as it was unable to find a “unifying” figure.
“Rather than splits, a much more favourable alternative might be for the Labour Party to have a leader elected by MPs and a leader in the country elected by the entire membership,” said Mr Field in a letter to The Independent.
“Both would be key positions, but the electorate would be voting on the parliamentary team as an alternative government. How one gets there, of course, is another matter.”
Mr McDonnell responded: “What Jeremy demonstrated yesterday is an overwhelming majority in every section of the party - amongst the members, on the National Executive Committee and amongst members of the Parliamentary Labour Party and the shadow cabinet - he had a majority in every part of the party. He leads the party.”
Meanwhile, the shadow foreign secretary’s niece Emily Benn demanded a retraction from SNP MP George Kerevan over a “deeply offensive” tweet claiming her grandfather, left-wing stalwart Tony Benn, “must be turning in his grave” over his son’s pro-war stance.
Shadow work and pensions secretary Owen Smith, who opposed air strikes, branded Mr Livingstone’s backing for deselections “disgraceful”.
He told BBC Radio 4’s World At One programme: “I think that’s a disgraceful thing to say, and I certainly wouldn’t support that in any way, shape or form, and I don’t think that is reflected by a majority or even a significant minority in the Labour Party.”
Mr Smith said abuse of MPs who backed air strikes was “despicable”.
“The people who voted with the Government yesterday evening did so with good conscience and on the merits of the case that they saw, and I know many of them wrestled with that decision,” he said.
“We must not in any way demean them for making that absolutely justified and understandable decision.
“There is no room in our party - of all parties - for abuse.”
Asked whether David Cameron was concerned about reports of MPs being bullied, a Downing Street spokesman said: “The Prime Minister’s key view on this is it’s fundamental that MPs are able to express their views and set out their positions in the House on issues of great importance such as the debate we had yesterday.”
Some MPs have said that messages attacking them came from social media addresses that appeared to be linked to Momentum, the organisation set up by Corbyn supporters in the wake of his successful leadership campaign earlier this year.
But in a statement, Momentum said: “Momentum strongly disapproves of anyone who engages in abusive behaviour towards MPs or anyone else, and threatening or bullying, whether they are outside the Labour Party (as most are) or inside it. We specifically asked our supporters to emulate Jeremy Corbyn, and to keep their messages about the issues and to refrain from any personal attacks.
“Momentum is not a threat to MPs who voted for bombing. We have made clear that we will not campaign for the deselection of any MP and will not permit any local Momentum groups to do so. The selection of candidates is entirely a matter for local party members and rightly so.”
The Socialist Party published the wording of a model resolution which they suggested Labour members could use to demand the removal of their constituency MP.
Socialist Party member Nancy Taaffe said: “It is absolutely crucial that Labour MPs or councillors who use their positions to vote for this war - not to mention the destruction of jobs and services through cuts - should be held democratically accountable via a reselection process.
“MPs who refuse to carry out the wishes of the people they claim to represent and instead pass on, vote on and support Tory austerity and war can expect anger from constituents. We are calling for votes of no-confidence to be taken as well as lobbies of MP surgeries and constituency offices.”