German, Michael Schumacher, 43, who worked his way through the field from 22nd on the grid to finish 10th, for Mercedes, complained after Sunday's Bahrain Grand Prix that the current tyres prevented all-out racing and were turning F1 into a tyre-conservation contest.
Schumacher said: "The main thing I feel unhappy about is that everyone has to drive well below a driver's, and in particular, the car's limits to maintain the tyres.
"I just question whether the tyres should play such a big importance, or whether they should last a bit longer - and that you can drive at normal racing car speed and not cruise around like we have a Safety Car."
Pirelli said they were surprised at Schumacher's criticism although it has been clear in the opening four races of the year that tyre-preservation has become one of the most important strategic elements in the racing.
Pirelli director of motor sport Paul Hembery said he was taken aback especially because Schumacher had been happy with the tyres during winter testing.
He said: "I'm disappointed to hear those comments from someone of Michael's experience.
"Others were getting on with the job and getting their tyres to work. His comments during winter testing were that he was very happy with the tyres and now he seems to have changed his tune."
Schumacher added that he felt Pirelli should reconsider their approach to tyres because the problem of not being able to push to the limit was experienced by too many people.
He said: "I'm not happy about the situation, lets see what happens in future.
"If this was a one-off car issue, then you could say it's up on us to deal with it, but basically it is everybody, with maybe one or two exceptions.
"And if it is 80 per cent of the field that has this problem, then maybe the tyre supplier should think about that."
Sunday's race was dominated by tyre preservation and tyre management.
Apart from the technical and performance issues that forced many drivers to drive cautiously, and not race with abandon, the tyres also created more pit-stops that, in turn, upset the potential of certain drivers.
The victorious defending double world champion German Sebastian Vettel admitted that his fast start from pole had enabled him and his Red Bull team to control their tyre situation more comfortably than those chasing behind him.
Second-placed finisher Finn Kimi Raikkonen of Renault started the race from 11th on the grid after deciding to save four sets of new tyres for the race instead of pushing hard for a better qualifying position.