The Grecians looked to be on course for another defeat before Eliot Richards capitalised on goalkeeper Chris Lewington's fumble to bundle the ball home.
Tom Nichols had given Exeter the lead but Dagenham hit back early in the second half through Luke Norris and a contentious penalty scored by Medy Elito.
"It was a really good game of football and possibly our best performance at home probably since the autumn," Tisdale said. "I am really, really proud of the players and I know we scored late, but my God did we deserve a draw. It would have been a travesty if we had drawn the game.
"I like them (Dagenham), I like the way they play and the way their manager conducts himself and I thought it was difficult for both teams in very difficult conditions, with the pitch very bumpy and the mud beginning to go quite hard.
"But I thought our players were terrific considering, they gave absolutely everything and were tough and I would have been feeling particularly sorry for myself had we lost the game.
"The penalty sums up our season really, we don't seem to get any decisions. Perhaps it's the way we conduct ourselves.
"We had such a good couple of days leading up to the game as a squad, it would have been a real kick in the teeth if we had lost the game."