Mancini has already invested heavily in the squad, bringing in Yaya Toure, David Silva, Mario Balotelli, James Milner, Aleksandar Kolarov, Jerome Boateng and Edin Dzeko in the last 12 months, but he believes City lack the strength in depth of Manchester United and wants to spend again this summer.
"For us to stay near the top for a long time was good but during a moment in the season, like February or March when we played Europa League, Premier League and FA Cup, we played every three days," he said. "It's very difficult if you don't have a big list of players - it's impossible to go on for the final of these cups and play for the title.
"United will play eight or nine different players from the side that played Schalke for the match against Chelsea. They can make these changes and still win.
"I think we have a good team. We should improve - if we buy other players - because when you play in the Champions League every team is strong."
City are rumoured to be competing with United for the signature of Chile winger Sanchez and, asked about the player, Mancini said: "Sanchez is a good player."
Mancini believes it is essential City claim the FA Cup when they meet Stoke at Wembley on May 14 if they are to compete with the very best.
"It's crucial for us to win the FA Cup, then next year we can improve our squad and get other players," he said. "If we want to play for the title next season, it's very important to start to win something. Then, in the future, Manchester City will be a strong team in Europe."
Asked if City could win the title next season, Mancini said: "It depends on the next eight days but I think so."