Dave Challinor was proud of his Hartlepool team and the club's fans despite the National League side going down 4-1 at Sky Bet League One promotion chasers Oxford.
Pools led for nearly three-quarters of an hour after Mark Kitching slotted home in the ninth minute, pouncing on a back-pass from Rob Dickie.
But after Rob Hall levelled seven minutes into the second half, it was all Oxford.
Shandon Baptiste scored a brilliant second goal 14 minutes later and two late goals from Tariqe Fosu and Matty Taylor from the penalty spot gave Karl Robinson's team an ultimately comfortable passage into the fourth round.
Challinor said: "Of course you dream a little bit when you are leading. Unfortunately for us we didn't keep them frustrated for very long in the second half.
"I'm disappointed with the end result but unbelievably proud of what the players have done, and of our fans.
"They were unbelievable. I'm just sorry we couldn't hang on to give them something more to shout about.
"I'll take the hit for the last two goals because I wanted us to keep going for it at 2-1 down. And we probably tired the last five minutes.
"Oxford are the best team in League One by a mile. You don't push a strong Manchester City side the way they did without being very good players.
"I think they put the stats from the Man City game – like their 18 shots against them – in the programme to frighten us!
"It's the end of this competition now for us and we've got more important things to think about.
"We've got to use this experience as motivation for our players – to aspire to be as good as the Oxford players."
Oxford manager Robinson said: "It was a ridiculous error from us in the first half.
"But it was just about discipline. We have an identity now, for the first time in many years at this club, a way of playing, and we stuck to it which made them tire and gaps open up.
"We didn't get carried away, we stuck to our guns.
"I had a bit of a go at them at half-time because we were taking a while to do things. But I'm really happy with the way we played in the second half."
Baptiste's goal was a brilliant solo effort, and Robinson enthused: "The kid is a special talent.
"When I first came here he was out on loan to Hampton & Richmond. To see his journey over two years has been amazing.
"He scored a great goal against West Ham too, so he clearly loves the cups!"