Mr Shapps said the primary cause of the crisis had been the pandemic which had led to the cancellation of 30,000 HGV tests last year resulting in a shortage of qualified drivers.
However, he acknowledged that Brexit – which has cut the number of foreign drivers – had had an impact.
“Brexit I hear mentioned a lot and it no doubt will have been a factor," he said.
“On the other hand, it has actually helped us to change rules to be able to test more drivers more quickly.
“So, it has actually worked in both ways.”
His comments come after the favourite to succeed Angela Merkel as German chancellor suggested Britain’s shortage of lorry drivers is a result of Brexit.
Olaf Scholz, the leader of the centre-left Social Democrats, said that ending free movement of labour with the EU had created a “problem” for the UK.
“The free movement of Labour is part of the European Union,” he told reporters following Germany’s inconclusive elections.
“We worked very hard to convince the British not to leave the union. Now they decided different and I hope they will manage the problems coming from that.
“I think it’s constantly an important idea for all of us to make it happen that there will be good relations between the EU and the UK.
“But this is a problem to be solved.”
Mr Shapps condemned motorists who tried to fill up plastic water bottles with petrol as the panic buying continued.
“It is dangerous and extremely unhelpful,” he said.
Mr Shapps rejected criticism that the Government has been too slow to mobilise the Army to help deal with the fuel crisis.
Ministers announced on Monday they were putting troops on standby to deliver supplies as filling stations continued to run dry.
In a pool clip for broadcasters, Mr Shapps said: “There is a series of escalations that you go through in a crisis like this.
“We have already put 18 different steps in place which stretch right the way back to the spring.
“The system was just about coping until last weekend and it would have been capable of continuing to do so.
“Unfortunately, as we have seen with toilet rolls and other things, once people start to pursue a particular item, it can quickly escalate.
“But there is only so much petrol you can transfer into tanks. That is starting to work its way through.”
He said there are “tentative signs” that pressure on filling stations is beginning to ease.
Mr Shapps said there was more petrol in the filling stations, although he acknowledged it would not have an immediate impact on the queues for fuel.
“There are now the first very tentative signs of stabilisation in forecourt storage which won’t be reflected in the queues as yet,” he said.
“But it is the first time that we have seen more petrol actually in the petrol stations.
“As the industry said yesterday, the sooner we can all return to our normal buying habits, the sooner the situation will return to normal.”
Germit Mudhar, 61, a builder who requires a van for work, said the Government had been “running around like headless chickens” in response to public anxiety over fuel shortages.
“It’s ridiculous. The Government has messed it up, they never think about things seriously,” he told the PA news agency at a petrol station in London.
“First with food shortages and food shops… nobody seems to have a clue.
“They’re a bunch of idiots, they couldn’t foresee this and they’re running round like headless chickens.
“It’s one thing after another, they say they’ll do this and they’ll do that.”
Asked about public over-reaction to alleged fuel shortages, he added: “It’s not so much the panic buying, it’s not just that, the Government has known about the driver shortage for months and months and months.”