Under fire for the quick-wearing 2013 compounds that led to a blizzard of pitstops in Spain on Sunday, Hembery warned that a current testing ban made it harder for the Italian company to meet significant technical challenges coming in 2014.
He raised the possible scenario of a race "where you literally can only do five or six laps on every single option that we bring because we've totally underestimated the impact (of the new regulations).
"I don't think we'll have an issue with structural integrity but we could end up certainly with a compounding issue where we have completely the wrong compounds for the track or what's going to be the influence of the powertrain on the tyre," Hembery told Reuters.
"There are championships, less visible than F1, where those sorts of things have happened and you've ended up having to take 10 laps off the race distance and things like that."
Team managers held a sporting working group meeting at the Spanish Grand Prix and voted to maintain a ban on in-season testing, despite opposition from some teams.
McLaren's sporting director Sam Michael said they had decided to stay with the limit of 12 days pre-season, but testing in January was allowed and could be outside of Europe.
Pirelli currently have a 2010 Renault, up to five seconds a lap slower than current cars, for testing. They are expected to continue as sole tyre supplier in 2014, although a deal has yet to be signed.
"We have absolutely no in-season testing, we can't have access to these cars going around now and have to run around in a 2010 car. It's alright to sit there and criticise but you're not exactly given the tools to do a precise job," a defensive Hembery said at the weekend as criticism mounted.
Sunday's race in Barcelona put Pirelli even more in the spotlight with four pitstops turning out to be the norm and a number of failures in practice and the race that saw treads coming away from the tyres.
Pirelli went more aggressive with the tyres this year and have now agreed to change both the structure and compounds to make them last longer and reduce the number of pitstops.
A spokeswoman said on Tuesday that the modifications could be made from Canada, race seven of 19, next month rather than the end of June.
Next year sees a switch from the 2.4 litre V8 engines to new 1.6 litre V6 units with kinetic energy recovery systems and turbocharger.
"We are getting varied data from different teams which means there are going to be some surprises," said Hembery of the 2014 changes. "We don't want to be as a tyre maker in a situation where we come up with some surprises when we get to Melbourne (for the start of the season). We want to know before."
Ferrari, who have their own test track and one of the biggest budgets, have long pushed for a return to the in-season testing that was banned in 2009 to cut costs.
Hembery said Pirelli had different reasons and need to test with current cars, both now and in future.
"Next season if all we have available to us is a 2011 car, that's going to help us with nothing when you've got a very different powertrain," he said.
"I think they (the teams) are going to have to go back and revisit it (the ban). I don't think Ferrari and some of the other teams are going to let it go," added the Briton.
"I am hopeful that we can have some sort of compromise agreement where we can have some sensible, limited in-season testing."
- Sports & Recreation