Roberto Mancini believes Manchester City's season will take on a new complexion if they beat Chelsea in Sunday's FA Cup semi-final and win the trophy in next month's final at Wembley where they would face either Wigan Athletic or Millwall.

City trail Manchester United, whom they defeated in Monday's derby, by 12 points in the Premier League with the manager accepting the title defence is all but over. Asked if winning the Cup and finishing second would alter how the campaign is viewed, he said: "Yeah, for sure. It is very important to continue to win trophies. I don't think it will be easy because Sunday will be a difficult game. But it will be important."

If City win the Cup it would be Mancini's third major domestic honour in his three full seasons at City. Yet with speculation surrounding his position, the Italian denied there was any more pressure for him or for players whose own futures may depend on winning the trophy. "It will only be the same pressure that any team would have playing in a semi-final," he said. "It is important that we have the same concentration that we had against United and we play the same football we have played in the last two or three weeks. It is important that we have a good attitude for this game.

"It is important for me, for the players, for the club because it is another semi-final and we have the chance to reach another final and to win another trophy."

David Silva's hamstring injury makes him a serious doubt to face Rafael Benítez's side. "We decide on Sunday morning. We don't know if it is possible but if there is a risk he doesn't play. It is getting better. Yesterday he ran – I think we have a chance," said Mancini, who was more optimistic about Sergio Agüero, scorer of the winner against United. "I am happy because he had a good impact on the game on Monday night. It is important he didn't have any problem in his knee – probably is not 100% but Sergio 80% is important."

City impressed in the derby victory and Mancini wishes his side had performed like that more often during the season. "I feel frustrated because if we had played at our best in some games we would have picked up important points for the championship. But we had a difficult moment when we played QPR, Liverpool and Southampton. We dropped seven points in those three games and that made the gap too big. There are some moments in the season when it is not important if you play well or not – it is just important that you win. Instead we lost points.

"I think [the derby win] was important for the next game that we have in the Premier League, and Cup. The championship is not important, it is finished but it is important we showed we are like them. For us it is only important to reduce the gap because we don't deserve to be 12 points behind."

Along with Joleon Lescott and Carlos Tevez, Gareth Barry will have a year remaining on his deal this summer. Does the manager want the midfielder to extend his time at the club? "We have several players in this situation and we will sort this out in the next month but these players are important players for us," he said. "I'm very happy with Gareth because he is a good guy and a serious professional player."