"The results have not been going our way in the last few games and we were really trying to make it right," Sterling told the club's website (www.mcfc.co.uk).
"It's (Tuesday's win) a massive, massive lift obviously. The players that we got here we expect to win every game. Going into the game against Swansea, we know we can win the game and we just need to go out there and play our football.
"Not really concentrate what's going on elsewhere in the league."
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Needing a win to have any chance of pipping Juventus to top spot in the Champions League, City trailed 2-1 at half-time after David Silva's opener was cancelled out by goals from Julian Korb and Raffael.
Sterling, who grabbed the headlines after scoring twice in as many minutes in the second half, attributed their comeback to the half-time team talk given by midfielder Yaya Toure and the senior players in the squad.
"There was definitely a great connection in the changing room with the team talk from Yaya and the boys to dig deep if we needed to and that's what happened today and it's a credit to the spirit in the camp," Sterling said.
"This is a team that's going to score goals. We just got to, on the whole, be more solid and try to keep more teams at bay and I think we can to that and it's just a matter of time."
(Reporting by Shravanth Vijayakumar in Bengaluru; editing by Sudipto Ganguly)
