The Catalan giants have been one of the dominant forces in Europe in the 21st century, while City have struggled to make an impact in the Champions League despite massive investment from their Qatari owners.
However, the Barca chief believes the situation could well change over the coming years as City and PSG continue to draw on their "unlimited resources."
"The emergence of Manchester City and Paris Saint-Germain has made things more difficult," Bartomeu told BBC.
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"Of course we are a very big club. We are the biggest club in the world, but when we compete with unlimited resources we have to find other ways, other strategies."
Barcelona holds a 2-0 lead heading into the second leg of the club's Champions League round of 16 tie against Manchester City at Camp Nou on Wednesday.
PSG, meanwhile, is on the verge of booking its ticket for the last eight after a 4-0 first-leg win over Bayer Leverkusen.