Exeter-born Liam Sercombe scored his first goal of the season to give the Grecians a half-time lead, but Joe Lennox salvaged a point for the Pilgrims 16 minutes from time with his first goal in professional football.
However, Exeter were left cursing a bad miss by 15-goal top scorer Jamie Cureton just after half-time which would have given City a 2-0 lead.
Fletcher said: "I am pleased. They are in the play-offs and they are there on merit. They are a good side so we knew it was going to be tough.
"I was disappointed to go a goal down in the first half, I thought we were in control of the game at that point.
"We set up well and they changed their formation a couple of times in the first half to combat us and the goal was a little bit against the run of play.
"In the second half we came out on the front foot and put them under pressure and got the goal we deserved.
"We rode our luck a little bit but in the grand scheme of things an away point in the derby game on the back of a home win last week makes it a good day.
"We didn't want to go too gung-ho too early on. We have to be professional and keep our shape but once we got the ball down in the second half we were on top and we made a couple of substitutions to give us a little bit of impetus."
- Sports & Recreation
- Jamie Cureton