The Italian marque has been the subject of intense criticism of its controversial and heavily-degrading 2013 tyres, and is now embroiled in the 'test-gate' scandal and facing the charges of F1's governing body.
Former F1 team owner turned television pundit Jordan, however, says F1 should treat the maker of its tyres with more caution.
"Pirelli openly submitted its tender, they also paid money for it, and now they're criticised or ridiculed by some teams," the Irishman told Austria's Servus TV.
"I think some teams should be a bit more careful. Who is going to give them tyres if Pirelli is not there?" he wondered.
"Do we see anyone else willing to do a better job? I think we should really be a little more friendly to Pirelli," added Jordan.
He said it would be completely wrong for Pirelli to cave in to the loud protests of teams like Red Bull and agree to modify the 2013 tyres mid-season.
"You can't punish someone who's done everything right," said Jordan, referring to those teams who "built their cars correctly" for the 2013 specifications.
He said Canada was an example of teams only criticising the tyres when they can't make their cars work.
"I didn't hear a word about the tyres (in Canada)," said Jordan.
"Sebastian (Vettel) said nothing, Alonso and Hamilton said nothing, and these were the top three.
"They complain if it doesn't work out for them," he added.