Seven-time world champion Michael Schumacher claims Pirelli are supplying tyres that do not befit Formula 1.
Pirelli re-designed the tyres after being asked to produce ones that make racing more interesting, but Schumacher has complained about high degradation.
"I had to drive at a pace to manage the tyres to finish with tyres left over," he said. "We should question whether that should be the case.
"It's unsatisfying and not what a Formula 1 event should be."
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“This year I don't really know what to make of the tyres, but it's not an excuse because other people are doing a good job on them”
Schumacher finished 10th in Sunday's Bahrain Grand Prix, which was marked by the highest tyre degradation of the season so far.
The seven-time champion added: "If 80 or 90% complain, maybe Pirelli should think about it.
"I don't think it is right only one or two teams can handle it and the rest struggle so much."
Of the front-running cars, Schumacher's Mercedes has among the highest tyre usage.
The team struggled to varying degrees in the first two races in Australia and Malaysia, before coming good in China last weekend, only to suffer again in Bahrain.
Schumacher's team-mate Nico Rosberg, who won from pole in China in much cooler temperatures, finished fifth after starting from the same grid position.
Pirelli entered F1 in 2011 with a brief to provide tyres that went off more quickly than the Bridgestones the sport had used previously. The idea was to promote more pit stops and hopefully spice up the racing.
This year, they have changed the design, reducing the pace differential between the four dry-weather tyres in an attempt to mix up strategy more extensively.
"Michael is a professional racing driver and it's all about looking after the tyres. That's down to the car - the driver can't really do that. He can drive slower but then a lot of people will drive quicker and beat you. You've got to get the balance on the car right - and that's what Mercedes didn't do in Bahrain."
But teams and drivers have complained that they do not yet understand the tyres, which they are finding hard to keep in the right operating temperature.
That means that the performance of cars has fluctuated wildly from one race to another.
In contrast to Mercedes, Red Bull's car did not work so well in the cooler weather of China but proved the quickest in the hotter conditions of Bahrain.
McLaren, who were competitive in the first three races, struggled badly at the weekend.
Jenson Button said: "Last year, we knew the tyres had high degradation but we understood them. This year, I don't really know what to make of the tyres, but it's not an excuse because other people are doing a good job on them this weekend."
Pirelli motorsport director Paul Hembery played down the criticisms of Schumacher and Button, insisting that coping with tyre changes was a fundamental challenge of the sport.
"The competition has never been closer and part of that is down to the fact that everyone has exactly the same opportunities and challenges with the tyres. It is down to them to make the best of it," he said.
"Formula one has always been a meritocracy - in the end the best engineers and drivers will always succeed."