Liverpool dispatched City in the quarter-finals, following up their 3-0 victory at Anfield in the first leg by triumphing 2-1 in the return match at the Etihad Stadium on Tuesday.
Oxlade-Chamberlain joined Liverpool from Arsenal for a reported £35 million in August and is elated the switch has put him in a position to achieve one of his major goals.
"It is massive. It is everything you dream of when you are a young lad," he said.
"You want to play in finals and they don't come much bigger than the Champions League final.
"We've made my dream that one step closer by getting into the semi-finals. We have given ourselves a great opportunity."
The successive triumphs over City, as well as a 4-3 victory over the Premier League champions-elect in January, have buoyed Liverpool, who Oxlade-Chamberlain suggested fear no one in the final four.
"To beat City twice is no easy feat. We did it twice in a week and we also did it at an earlier stage this season," said the England international.
"It just shows to us that when we are at the races and at the right level we can beat anyone in this league.
"Now it is on us, whoever we get in the next round, to go and prove that we can beat people in Europe as well. It's going to be tough whoever you play. People might say Roma [are the preference] but look what they did [eliminating Barcelona], they performed amazingly well and look a great side.
"It doesn't matter who we get now, we have to make sure we are ready for anyone and can beat anyone."