The four-cap Serbia international arrived in Sydney on Sunday after signing with the Sky Blues from J-League giants Urawa Red Diamonds.
Despotovic is expected to come off the bench in Saturday's home clash against Wellington Phoenix and is excited at the club's prospects this season.
"My first impressions of the club are really good, fantastic," he said.
"I hope that we can fight this year for the championship and because of that I am here.
"I'll try all my best to win the league, with these big stars here, there are a few players who played for the (Socceroos) before, some young players and big stars, so I think that we don't have an excuse.
"I thought it was going to be more difficult (to settle in) but all of my colleagues and people from the club have helped me a lot and I'm really enjoying these first few days."
Asked what his personal expectations for the season are, the 30-year-old replied: "When a striker comes to a team always they expect him to score goals.
"The only thing that I can promise from my colleagues and people from the club is that I'm going to fight for this club, I'm going to give all my best and try to win every game and if I score goals that will be fantastic too."
Farina is also expecting goals from his new signing but urged Sydney FC fans to patient with their new star.
"His arrival helps freshen up the squad in terms of options for us up front and obviously we brought him here to score goals hopefully," Farina said.
"Strikers will always want to score ... and expectation as we know here are pretty big but we can't expect too much too early.
"He won't start (against the Phoenix) but we'll make a decision prior to kick off whether he will sit on the bench or not, but there is every chance.
"He arrived Sunday ... and there's no mad rush at the moment. We want to get him into the swing of training and get him ready basically rather than taking any risks but I'm pretty positive that he should be right for the bench."
The Sky Blues are coming off back-to-back wins and thumped the Phoenix 7-1 in Sydney last season, but Farina declared Saturday's clash against Ernie Merrick's men a danger game.
"Wellington is potentially a banana skin for us and we've got to make sure that we're focused and ready to go," he said.
"I think they're a better side this year than they were last year. They've most probably been a little bit unlucky with some of their results but they've got some good players who can hurt you."