"We will dedicate the win to Ron," said Trollope, acknowledging the man who had been on the Pirates' board since 1986 and died the day before the game.
"It wasn't a performance he'd have liked, but we got the three points for him.
"He countersigned my first contract and was chairman in our promotion year - he was very close to a number of the players and up until a few years ago, he was the one who would travel on the coach with the team. He will be sorely missed."
On the match Trollope continued
"We were very pleased with a clean sheet - it had been a long time coming.
"We had been on a bad run and we are not suddenly going to start playing at our flowing best, but that was our third home win on the trot.
"We know we didn't fire at all - we didn't get out passing going.
"Exeter showed what a good side they are and we knew we would be in for a test. They will feel hard done by going away with nothing, but it's an excellent sign if you can win when you are not firing on all cylinders.
"They forced us back and had a lot of possession in midfield, but we were good in both boxes and it's the three points that matter.
"There have been plenty of times in the past few seasons when we have played very well but not got what we deserved.
"I'm far from happy, and the players were happy we won but disappointed with the performance. A few were almost down about it and it wasn't like a winning dressing room. They know there is a lot to improve on.
"We were forced back and our energy levels didn't look as good as they usually are."
Exeter boss Paul Tisdale said: "I don't think there's any doubt the better side lost - I was proud of the players.