Chris Burchell, managing director at Arriva, which runs the under-fire franchise, said a new plan was needed for its services as he was grilled by northern political leaders over its poor performance today.
As criticism mounts over the services provided by Northern and fellow operator TransPennine Express (TPE), Greater Manchester metro mayor Andy Burnham said a public deadline should be set for TPE to improve.
At a meeting of the Rail North Committee, TransPennine bosses blamed its poor performance in late 2019 - when it was the worst-performing operator in the country - on Spanish manufacturer CAF's failure to deliver new trains.
And officials at Northern said the cancellations and disruption on its services before Christmas was a result of "unprecedented" levels of sickness among its drivers.
But the explanation was ridiculed by Mr Burnham, who told the meeting in central Leeds: "It is not an excuse we would accept from any other public organisation, why would we accept it from you if you wouldn't accept it from us."
As he was quizzed over his perceived lack of public involvement in improving Northern services, Mr Burchell said it had been forced to adjust its plans because a number of promised infrastructure schemes have failed to materialise.
He said the plan for services agreed when the Northern franchise was awarded in 2015 was to improve capacity for passengers and create more journeys.
Mr Burchell said that since then 2,000 more trains a week are in service but the improvements depended on "other things happening and not all those things have taken place".
By May this year Northern has promised to remove all of its hated Pacers and to introduce a new hourly service between York and Scarborough.
But Mr Burchell said: "We are trying to run more trains on a network that has not been changed as originally envisaged."
He said the original franchise plan "has essentially become undeliverable" but added: "I don't think any other operator could have made better decisions than we have."
TransPennine and Northern bosses both apologised to customers during the meeting today.
But Northern was warned by committee chairman Liam Robinson: "This is one minute to midnight, the travelling public are sick and tired of two years of chaos. You need to buck up your ideas and deliver a more reliable service."
He said in the coming days northern political leaders would be issuing a public deadline for TransPennine to improve.
Mr Robinson added: "We don't want to accept any more apologies for poor performance. It really does need to improve. If not we will be asking for a different organisation to come in and run rail services."
TPE announced this week that it would issue refunds to season ticket holders as its recent performance was described as "completely unacceptable" by the Department for Transport (DfT).
Its managing director Leo Goodwin said the late introduction of new trains was the biggest single factor on its performance, while a lack of reliability had disrupted driver training.
He said these issues were now being resolved and he hoped that in the coming weeks TransPennine's performance would return to the levels seen in early 2019.
But Mr Burnham told him a public deadline would soon be set for things to improve, adding: "We are not prepared any longer to put up with the misery that you are inflicting on people in the North."
Leeds City Council leader Judith Blake told TransPennine bosses: "You have come here today seeking to reassure us that you have matters in hand and that you have a grip on things.
"We are not reassured and won't be reassured until we actually see improvements every day across the network and the travelling public are getting where they need to every day."
The firm announced earlier this month that it has cancelled dozens of services and Transport Secretary Grant Shapps said he wanted an urgent meeting with the operator to discuss its services, described by a boss of the firm as "not up to scratch".
Office of Rail and Road figures show just 56 per cent of Northern trains arrived at stations within one minute of the timetable in the 12 months to December 7, compared with the average across Britain of 65 per cent.
TPE's three per cent rebate to season ticket holders comes after issues with the introduction of new trains.
The operator said the late delivery of some of the new trains, a maintenance backlog and infrastructure issues, causing a delay in crew training, meant it had to run a temporary decreased service after a number of cancellations.
On Monday, Mr Goodwin said the firm had introduced an "amended timetable between Liverpool Lime Street and Edinburgh for the rest of January" to allow "services to recover" and "consistency for customers" while the new fleet of trains is rolled out.
Changes listed on the firm's website showed they involved dozens of services across the network.
A DfT spokesman said on Tuesday: "TransPennine Express's performance in recent weeks has been completely unacceptable."
The Yorkshire Post today revealed that Northern has been condemned by transport bosses for a "fundamental failure" to deliver on the promises made to passengers when it bid to become the North's biggest rail operator.
A confidential report seen by this newspaper reveals that Northern bosses have asked to be allowed to miss the targets set out in their franchise agreement by as much as 21 months.
As pressure mounts on Transport Secretary Grant Shapps to strip Arriva Rail North (ARN) of the franchise because of its poor performance, the firm is revealed to be "significantly late" in refurbishing its fleet of trains.
Only 3.5 per cent of the digital improvements which should have been delivered by January 1, including the provision of on-board WiFi, have been made, while a number of trains have yet to have new seat covers and cushions or be given a deep clean.
The failings were discussed by the Rail North Committee but in a session held behind closed doors.
Mr Shapps says he is taking steps that could lead to Northern losing its franchise, including its services being brought under government control.
He had been listed as attending on the agenda for this afternoon's Transport for the North meeting in central Leeds.
But it is understood that rail minister Chris Heaton-Harris will actually be attending, with the Transport Secretary instead set to visit Leeds on Thursday.
The results of the government-commissioned Williams Rail review, which is expected to recommend the end of the current franchising model, will be published later this year.