The Italian company's motorsport director Paul Hembery hoped that would not be the case, however.
"There have been concerns from some of the teams that the changes will favour one team or another, but we don't think that will be the case," he told the autosport.com website.
"These changes are being made for Pirelli, not for anyone else. We need to get the balance right."
Pirelli announced earlier that changes to the structure and compounds of the tyres would be made for the Canadian Grand Prix in Montreal, the seventh of 19 races this season, on June 9.
They had said at the weekend that the new tyres could not be introduced until the British Grand Prix at the end of June but changed their minds after a review of the situation following Sunday's race in Barcelona.
The Italian supplier came in for considerable criticism from Red Bull, whose triple champion Sebastian Vettel saw his lead trimmed to four points over Lotus's Kimi Raikkonen, after a race fill of pitstops with Ferrari's Fernando Alonso making four on his way to victory.
Red Bull's billionaire owner Dietrich Mateschitz was quoted by Austrian media as saying Formula One had "nothing to do with racing anymore" while drivers complained that they had to slow to manage the tyres.
Formula One's commercial supremo Bernie Ecclestone also weighed in, telling Britain's Daily Express newspaper that "the tyres are wrong, not what we intended".
Mercedes and McLaren have also struggled to get to grips with the tyres this season while Ferrari, Lotus and Force India have managed to work well with them.
Pirelli said the changed tyres would have a revised construction using elements from the 2012 and 2013 tyres to ensure both durability and performance and reduce the number of pitstops.
"We didn't want to over-react, because by doing that we could then be helping certain teams," said Hembery, adding that he hoped the more durable rubber would not allow one team like Red Bull to dominate.
"But of course we always face that risk," he added.
Hembery said the pressure from Red Bull for the change had "not been excessive".
Red Bull principal Christian Horner told the dailymail.co.uk website that the effect of the changes on his team was impossible to predict.
"I think it will be in the interests of good racing over the next few grands prix," he added.
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