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.
|Tweet Ruud Gullit!
|Send your questions to AC Milan legend Ruud Gullit via @Heineken using #sharethesofa on Wednesday evening|
"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 defend a 2-0 lead in the second leg of their Champions League round of 16 tie against Manchester City at Camp Nou on Wednesday.
PSG, meanwhile, are on the verge of booking their ticket for the last eight after their 4-0 first-leg win over Bayer Leverkusen.