Spurs needed extra-time to win 3-0 via an own goal from Nathan Tshikuna, before the visitors struck through Dejan Kulusevski and Brennan Johnson.
Peaks said afterwards: "Be disappointed because we were that close to causing a massive upset, but equally be massively proud.
"Everyone put a shift in and when you look at the team we were up against, it was unbelievable from our boys - I am so proud of them.
"We had chances, the keeper made saves but what was brilliant is we were in the game right till the end.
"We knew it was going to be tough. I wanted people to see what we were about, and I think we have done that.
"I wanted to come here and talk to you guys and be proud of what I have seen - I am immensely proud.
"To get a home draw was better. The chance we had to level it was them coming here. They have been so respectful and to bring a team like that says a lot.
"I cannot knock them."