Lengthy queues have continued to form at petrol stations across the region after hundreds of sites ran dry due to chronic supply shortages.
The Government says the lack of petrol is down to panic buying and urged people to "calm down" and only buy the amount they need.
But critics have questioned why ministers did not foresee the problems, which have largely stemmed from a lack of available drivers for HGV petrol tankers.
Former transport minister John Spellar, the Labour MP for Warley, said the issue had been compounded by a failure to get licences back to HGV drivers that had been suspended for medical reasons.
"There is also a failure on the part of companies to train enough drivers," he added. "But this shortage of lorry drivers hasn't just come out of a clear blue sky, it has been building for years because companies have been happy to fill the gaps from abroad.
"There are questions to be answered as to whether anyone was keeping an eye on this. The question for the Department for Transport, is when did they know this driver shortage was looming, and what did they do about it?
"[Transport Secretary] Grant Shapps has been asleep at the wheel."
Stuart Anderson, the Conservative MP for Wolverhampton South West, said the issue stemmed from a "couple of supply shortages" reported by the major petrol firms which should not have had an impact on the general public "in any way, shape or form".
"Unfortunately people panicked and it led to a frenzy, which has resulted in the situation we are in now," he said.
"People need to just get what they need for now and to not fill up extra jerry cans to use up all the supplies.
"I'm hoping things will level out over the next few days and that we can return back to normal."
In a bid to address the crisis ministers have suspended competition laws to allow oil firms to target fuel deliveries at petrol stations, and also announced plans to issue temporary visas to 5,000 truck drivers from the EU.
Shaun Bailey, Conservative MP for West Bromwich West, said: "It has been made clear that there is not a fuel shortage in the country.
"My overall message is that people need to stop panicking and to stop queuing for hours on end at petrol forecourts. It is a ridiculous situation that has been whipped up by all sides.
"We have got to remember that at the end of the day it's not just consumers in cars that need this stuff, it's emergency vehicles, it's the NHS. By panic buying, those are the people who are being denied the opportunity to get fuel.
"The pragmatic measures the Government has brought in are the right ones to try and get on top of this situation. If we all take a sensible approach to how we buy fuel we can help to get things back to normal as quickly as possible."
Wolverhampton South East MP Pat McFadden, the Shadow City Minister, said: "For months the Government refused to address the shortage of HGV drivers.
"Time after time they turned down requests from the haulage industry to allow more drivers from overseas on a temporary basis. In digging in and refusing the industry’s requests ministers put ideology before the economic interests of the country.
"Now the Government has done a screeching u-turn when people are facing chaos at petrol stations. The Government needs to get a grip and sort out not just the fuel crisis but also the wider crisis problems in the supply industry.
"People don’t want governments to deliver the earth but the public does have a legitimate expectation to be able to buy a chicken and fill their car with petrol."