The Hampshire side led twice in an amazing first half at Anfield, and Liverpool were fortunate to be level at the break.
Havant scored through Richard Pacquette early on and an Alfie Potter strike was deflected home by debutant Martin Skrtel.
But nobody can take anything away from a brave performance by the Hampshire side, which certainly scared Liverpool.
Gale said: "I'm proud of my side to produce a performance like that.
"We were magnificent, and for the Liverpool support to give us a standing ovation at the end was fully deserved.
"People laughed when we said we were going to come here and have a go, but we did just that. We scored early on and it took Liverpool a long time to get back at us. That should have been the end of it, but we scored almost straight away and I am only disappointed that we let in an equaliser just on half-time.
"But we were playing against world class players, things like that are going to happen."
He added: "I'd told them we were not here for a jolly-up, we can have a party afterwards.
"There was also no point in just defending, we cannot change the way we play.
"If you sit back against a team like this you will be murdered, and we certainly were not murdered. The fears were that we could have got battered - but that did not happen and that is what has made me proud of my team."
Relieved Liverpool boss Rafael Benitez praised the non-league side, saying: "Credit to them, they did everything they could and when they scored early on it gave them a lot of hope.
"We were very disappointing in the first half, our defending was not good enough.
"But in the second period we believed they could not keep their high tempo, and that is how it turned out. When a team from their level scores twice at a place like Anfield, it means they can run further and for much longer.
"But the FA Cup is like this, it is a fantastic competition, when you see a club six divisions below us playing like that and giving everything it shows what a great competition this is.
"But we expected them to fight like that. We have watched them and seen how they beat Swansea, a team who are on top of their division and playing well."
He added: "From our point of view, we knew we had to improve in the second half, pass the ball better and show more movement.
"We knew they would be good at set-pieces, they were hoping for a breakthrough like that..
"But after the break we were able to control the game and get the result. But again, credit to them, they were outstanding."