Sergio Aguero scored twice with Leroy Sane, Pablo Zabaleta and Kelechi Iheanacho also on the scoreline as the high-flying Championship side were put to the sword in an impressive last 16 replay at the Etihad.
City’s reward is a quarter-final trip to face Premier League rival Middlesbrough a week on Saturday.
And given the rich vein of form Pep Guardiola’s side have struck, Sterling says he and his City team-mates are determined to repeat the Club’s 2011 FA Cup triumph.
“We want to compete in as many trophies as we can and the FA Cup is something we want to go all the way in,” said the England winger.
“We just need to keep going game by game and challenge in every one.
“They went 1-0 up and we were disappointed to concede early. They played well and were at us. But credit to the boys, we dug in and showed spirit.”
Sterling’s ambition was matched by two-goal hero Aguero who followed up last week’s Champions League brace against Monaco with another superb display that earned him the man-of-the-match award.
And the Argentine said he was satisfied both with his own and the team’s form as the season enters its decisive last third.
“I am very happy for the result and the two goal but especially for getting through to the next round,” said Aguero.
“I always try to do my best and do what the manager wants me to do.
“I want to make my manager happy with my performances.”
