The defending champions launched their Barclays Premier League campaign with a hard-fought 2-0 win at Newcastle.
Pellegrini was delighted with a victory which came despite many of his World Cup stars having gone into the game short of match fitness, but, while he knows there will be stiff competition once again this season, he is certain City have grown during his time at the club.
He said: "It's very difficult to compare each year. Maybe last year a lot of people doubted we could win the title because it was my first season here in the Premier League.
"Today, we have one year more working with the players and I think we have also a strong squad.
"But always in England in the Premier League, you have five or six teams that can win the title, so we need to have the same attitude as we had today, the hunger with which we have started the season, the same humility with which we played today in every game.
"I am sure this squad can fight, and we will see at the end of the season which titles we will win."
City got their noses in front when David Silva expertly converted Edin Dzeko's clever 38th-minute back-heeled pass, but they had to wait until stoppage time at the end of the game at St James' Park to wrap up victory.
Sergio Aguero secured the points with a close-range finish after goalkeeper Tim Krul had blocked his initial effort, although only a remarkable block by Fernando had denied Newcastle a late equaliser minutes earlier.
Pellegrini said: "I am very happy because I think it's always important to start the season winning, especially when you have to play away at so difficult a stadium as St James' - it's always a difficult stadium for every team that comes here.
"Maybe in the second half we couldn't have so much possession of the ball because seven of our 10 [outfield] players were not able to play 90 minutes at the same pace.
"But we were very concentrated, very well organised and we kept a clean sheet, and finally we decided the game with a second goal."
Opposite number Alan Pardew was able to take positives from defeat in a game which saw him hand competitive debuts to Daryl Janmaat, Jack Colback, Remy Cabella and Emmanuel Riviere, with Ayoze Perez and Rolando Aarons getting a first taste from the bench.
Pardew said: "I honestly feel we have come up against individuals today who we are not going to see every week.
"Some of their play is outstanding and you have only got to see it close up to know the quality of [Samir] Nasri and Silva, the power of Yaya Toure, and Dzeko up front is a real handful, and I thought we coped with it as well as we could.
"When you play the top teams, you need a break - there's no doubt about that.
"Whenever I have won against the tops sides, you get a break in the game and it didn't happen for us today. We didn't get a ricochet or something that fell our way.
"But I am as pleased as I can be with a 2-0 defeat."
Pardew was less than polite to his opposite number when the sides met on Tyneside last season, but there was no repeat this time around.
Pellegrini said: "I don't have any problems with Alan. It was a mistake that he made the other season, but he apologised in the moment, and I told him in the same moment, 'Don't you worry about that, it's finished and all forgiven'.
"There was no problem. He had a lot of problems last year - not only with me. It's a new season and everyone learns from things."
- Sports & Recreation
- Barclays Premier League