The brace took Sterling’s tally for the season to 18 goals and lifted him ahead of Sergio Aguero in the charts.
City's reward is an enticing two legged semi-final with United, with the first leg scheduled for Old Trafford.
But the England winger said his goals won’t mean anything unless City go on to claim some silverware.
And he insisted that City were looking to achieve success on all cup fronts, not just in the Carabao... a competition we have won for the past two seasons.
"It (finishing above Aguero) would not mean anything without silverware and then I'll be happy with my goal tally after that,” said Sterling.
“Every competition we’re trying to compete in. It's not just the Premier League, which I know that looks out of reach but we’re looking to get to finals in this, the FA Cup and even the Champions League."
It wasn’t all plain sailing for City. Oxford proved a real handful and Matty Taylor’s 46th minute goal brought them level before Sterling struck twice.
And Sterling was full of praise for the hosts – as well as the performance of teenage defender Taylor Harwood-Bellis who again impressed in the centre of defence alongside Eric Garcia and to whom he handed his own Sky man of the match award to after the game.
“They were still in the game. They equalised and made it difficult. Goals are goals, I'm in the team to do a job. I will always try and put them [goals] in.
"I don't need to nurture Taylor [Harwood-Bellis] or any of the other lads. They come through in training and do their job brilliantly."