Only 127 EU tanker drivers have responded to Government pleas to come to the UK to ease the fuel crisis.
Boris Johnson said fewer than half of the 300 visas offered to European drivers under an emergency scheme had been granted.
They are among some 5,000 visas offered to curb an acute shortage of drivers, which has caused chaos for food and fuel supplies.
The Prime Minister claimed that only 127 names had been put forward after reports put the figure even lower.
He told BBC Breakfast: "It's a fascinating illustration of the problem of the shortage.
"What we said to the road haulage industry was 'fine, give us the names of the drivers that you want to bring in and we will sort out the visas, you've got another 5,000 visas'.
"They only produced 127 names so far. What that shows is the global shortage."
Concerns about shortages of supplies have loomed large over Conservative Party conference in Manchester.
Mr Johnson claimed the economy has been in a "deep freeze and the pipes are unfreezing now", blaming the stresses and strains on the supply chain on the economy "waking up" from the pandemic.
Asked if Christmas would be better this year after the PM cancelled festivities last year, he struck an optimistic note.
"Christmas this year will be very considerably better than last year," he told the BBC.
"I think we have very reliable supply chains in this country."
He added: "There are obviously issues that we have to address, there have been shortages in lorry drivers around the world.
"There are shortages of lorry drivers in China at the moment because the world economy is growing again."
Mr Johnson claimed the shortages of the pumps were caused by "demand, not supply" at the pumps - and compared it to people making cups of tea at half-time in a cup final.
He told LBC: "I sympathise very much with the frustrations of people who have been queueing for petrol. I really, really do.
"I understand how infuriating it is when you can't get petrol at the pumps, but I must repeat that this has overwhelmingly been a problem of demand, not supply."
Mr Johnson added: "What I am getting at is that the tanker drivers, the lorry drivers, they have got more than the average week's supply to the pumps for the last few days, and that is the situation."
He also said: "I think even the Petrol Retailers Association have been saying that the situation has been improving markedly.
"What you are seeing is the UK economy coming back into life, really sort of stretching its legs, starting to move again, and of course there's been a bit of creaking here and there because we haven't had such activity in a long time."
