The gulf between the clubs seems large at present, Barca having beaten City four times in the Champions League over the past two seasons, comfortably ousting them from the tournament on each occasion.
The Spanish side are top of their domestic standings and hammered Bayern Munich 3-0 in the first leg of their Champions League semi-final, while City have surrendered their Premier League crown in fairly tame fashion.
However, Pellegrini pointed out that his club have come a long way in quite a short time and thinks there is even better to come.
"The project at this club is to improve every year,” said Pellegrini. “To grow every year as a club, in all senses, in every department, young players, first team.
"It's not easy to compare, not the whole history, but this club in the last seven years has had the amount of money you need to compete with Barcelona, Real Madrid, Bayern, Manchester United - the most important teams of the world that can spend more money and have the best players.
"Maybe a lot of people are nervous, because you don't do it in three, four, five years. All these projects need a long time and every year you must demonstrate that you are growing and improving.
"This season we are really seeing again the Barcelona we saw a few years ago.
"But there is a lot of things we can try to reduce the distance between our team and them. I am sure we are going to do it sooner than five years."
The great Lionel Messi was the key man in Barcelona’s win over Bayern and Pellegrini would love to have someone who could make a similar impact.
"First we need to find another Messi!” he said. “He makes the difference, without doubt, like (Cristiano) Ronaldo at Real Madrid.
"But last year Barcelona didn't win any titles. Messi is an important player but it's not just Messi, you need a lot of things around him to be an important team.
"I said when we played against Barcelona we were very unlucky, that both years we had to play against the best team in the world, with Messi included.
"I think what Barcelona did against Bayern is no surprise for anyone, and not to me. Now they are demonstrating that I was not so wrong in what I said."
Pellegrini thinks forward Sergio ‘Kun’ Aguero can be the key man for City in coming seasons.
The Argentinean has had another superb campaign but injuries have limited his impact to an extent.
Pellegrini added: “It's important for Kun to improve every year, to play all the games. Maybe next year we'll see another Kun because he is working differently, he is growing every year.
"I hope he will be as important here as those players are at their teams."