The Italian company was again in the line of fire at the weekend's Korean Grand Prix, with Ferrari's Fernando Alonso and Red Bull's Mark Webber complaining about how quickly the tyres wore out. (Agencies)
McLaren's Sergio Perez suffered an explosive delamination of his front right tyre during the race at Yeongam which left debris strewn across the track and brought out the safety car.
The incident was reminiscent, in terms of drama, of the spate of blowouts earlier in the season that triggered safety fears and forced Pirelli to return to last year's structure with 2013 compounds.
Pirelli motorsport head Paul Hembery told reporters on Sunday there were no worries about the Perez incident but there was real concern about how the tyres would behave next year when the rules change significantly and a new V6 turbocharged engine is introduced.
A planned tyre test with McLaren in Austin, Texas, before next month's U.S. Grand Prix was cancelled after objections that it could favour the former champions, who are fighting Force India for fifth place overall.
Pirelli have done several tests, including a controversial 'secret' one with Mercedes in May, with teams providing older cars, but have repeatedly complained that they need to use more representative machinery.
"We're running around in a 2010 car, developing tyres for the 2014 car, which nobody really knows what it's going to look like. Yet every time we even ask to test with a 2011 car we come up against opposition," said Hembery.
"Going forward, to do what we need to do, we need to have the ability to test and help everybody - drivers and teams," added the Briton.
"Whilst nobody wants to think they're going to get an advantage in testing, you can't carry on going round in circles and decide to do nothing. Something has to change," he said.
Hembery said Pirelli wanted to reduce the amount of 'marbles' - small chunks of tyre rubber - that litter the track and increase the mechanical strength of the compound.
To do that, they need to test at certain tracks with suitable conditions and also need teams to help them.
Sao Paulo's Interlagos circuit could offer one such opportunity after the season-ender there in November.
Another option would be for Pirelli to test in Bahrain in January before two more scheduled pre-season tests there with all the teams in late February and early March.
"Ideally at the end of the season we'd like to see some use of these (2013) cars because they're the best and the quickest we've got at the moment," said Hembery.
"It would make sense to use them because for the majority of the teams they'll be of little relevance anyway," he asaid.
Sunday's race at Yeongam was marked by high degradation and heavy stress on the front rights, with drivers talking afterwards about how their tyres were effectively 'dead'.
Asked whether Formula One, which will allow some limited in-season testing next year after banning it previously to save money, was getting what it deserved, Hembery smiled wearily.
"To an extent, yes. We're still talking about trying to sort testing out and we're in October. I just hope the engine manufacturers for next year have been able to do their work, and as they desire," he replied.
"Otherwise the conversations we'll be having might be with them next year - I hope not, for their sake," he added.
Hembery said the new engine was likely to see a dramatic change in the application and delivery of power.
Yet there were no plans to test tyres in wet conditions with the new cars before the start of the 2014 season, despite the regular risk of a tropical deluge at the second race in Malaysia.
"There are things, as a sport, we need to improve on, which is something that is starting to be recognised. A number of the team principals have said we need to do something differently, and we obviously agree with that," said Hembery.
The Italian company was again in the line of fire at the weekend's Korean Grand Prix, with Ferrari's Fernando Alonso and Red Bull's Mark Webber complaining about how quickly the tyres wore out.