Scott Doe scored the only goal of the game after five minutes when he crashed a near-post header into the back of the net from Matthew Saunders' well-flighted corner kick.
"We got our game plan spot on, which makes a change!" Burnett said. "It was an awesome display by our players and I can't praise them enough.
"It was a great start for us and it gave us something to hold on to. We didn't play brilliantly well, but the performance was brilliant and you need that in games when you are fighting for your life. We will take points any way we can.
"I know Exeter haven't been on a great run, but this is a difficult place to come and win. I know Paul Tisdale very well and I hope they do well because they play football the right way and they have some very good players.
"We are a young team and we got deeper and deeper and we showed some inexperience and naivety at times, but I thought we looked the more likely to score and we defended superbly."