The Grecians went in front when Craig Woodman's corner was diverted into his own goal by Matt Duke and Lawson D'Ath celebrated his debut with a headed second on the stroke of half-time.
Kyel Reid scored direct from a corner to give the Bantams hope, but further goals by Scot Bennett and John O'Flynn sealed an emphatic win for Tisdale's side.
"In the first half we were second best and conceding a goal straight from a corner is not good enough and the second goal wasn't great either," Parkinson said.
"Generally Exeter were the better team. We had the elements against us in the first half, but I have played in games like that where you have got to roll your sleeves up and got to be stronger than you would usually be all over the pitch.
"We gave ourselves a lot to do. I thought second-half we played well, we pinned them in and got some fantastic crosses into the box. We got the goal back and to concede the third so quickly was a real blow because the momentum was with us at that stage and we were really having a good spell in the game.
"So the third goal killed it. We changed it and chased the game again and got done on the counter-attack, so you can forgive the fourth one.
"First-half we were second best, second-half I thought we played well but we have to play well for the whole game because Exeter are a good side."