Terry was impressed with the resistance shown by their Championship hosts.
He told ITV1: "We found it hard in the first half, but that's what the FA Cup is all about.
"They were a good side and stayed solid. We tried hard to break them down in the first half and finally got a goal, then managed better in the second half.
"It's been an amazing day. When you come to grounds like this it's what the cup is all about - smaller clubs giving their all."
Preston boss Darren Ferguson was sorry to see his side exit the competition after such a battling display in which they were not short on chances.
"It's disappointing to go out of the cup," he said.
"I think the pivotal point was just before half-time and just after. We gave away a sloppy goal from a set-piece and that changed the game.
"When we had the ball we had to have the concentration, but we knew if we lost it we would end up losing a goal. That's what happened but that's just the way it is and we were up against world class opponents."