City only managed to finish fifth in the Premier League in 2009/10, despite the heavy investment of billionaire owner Sheikh Mansour.
Santa Cruz, who arrived from Blackburn last June, admits it was a disappointment not to at least qualify for the Champions League and has demanded improvements.
"It has been a very tough season with a lot of new players," he told a press conference broadcast on Sky Sports News. "A new team has been built up.
"We didn't achieve what we expected and of course we can't say that we are happy.
"I think that the pressure is going to grow for us because of the kind of money that the owner is spending on the club."
He added: "We expect next year to not only do well, but also to see if we can fight for the title."
Santa Cruz was an acquisition of former boss Mark Hughes following their successful time together at Blackburn.
But Hughes' sacking in December 2009, the striker's injuries and the appointment of new manager Roberto Mancini meant that first-team opportunities were not always guaranteed among City's squad of stars.
Santa Cruz, though, does not fear extra signings and expects more arrivals over the summer.
"I wouldn't be surprised to see a couple of famous faces around the club," said Santa Cruz, who is preparing for the World Cup finals with Paraguay.
"I think that once the market starts moving we will see more. But I am sure we will have new signings and new people coming."