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After an even first half, Charlie Cummins headed the Grecians in front with his first league goal, only for Ronan Coughlan to equalise three minutes later.
But a stunning 25-yard curler from defender Luca Woodhouse proved to be the winner for Exeter.
Taylor said: “It was not a pretty game in the first half, the conditions were always going to play a part and we knew that yesterday and Fleetwood played them better than we did in the first half.
“I liked us in the second half because we had more forward intent and more speed in our game. I think there was some respect shown by the opposition in the way they set up and we take that as a compliment, but we have to find solutions and ways to break teams down. But what we did in the second half, I am so proud of the group.
“We were a bit physically low in the first half and a bit of the ‘three-game week’ in that, but if we want to be a team that competes, then put physicality to one side, go as you hard as you can and go with it. Trust the attacking principles and our attacking play against teams that get bodies behind the ball.
“The conditions played a part in that first half, I was honest with the group in what I wanted at half-time, but they are a young group and I am so proud of how they came through because that was a good test for them today.”
Fleetwood boss Matt Lawlor felt there was nothing in the game and rued two moments where his side failed to deal with City’s threat.
“It was extremely frustrating because I didn’t think there was anything in it,” he said. “The conditions were minging and it came down to two moments, didn’t it? Two weak moments from us change the perception of the performance.
“I thought it was a disciplined performance for the large part, we had chances – a lot of chances in the last 20-30 minutes – but yet again, we haven’t looked after two moments.
“They took their opportunities but they didn’t cut us open. The first one, we have to get across the man and deal with the cross better and the second goal, they haven’t even engineered a chance. He has bundled through two of them, we need to win it and don’t and he curled one into the top corner.
“There is nothing in the game if you take those two moments away, but for us, we had enough moments to get back in it as well.”