Taylor's side were pegged back by Francois Zoko's strike but on-loan midfielder John Mousinho scored his first goal for Gillingham to give them a crucial victory.
"I don't think we deserved to be 1-0 down at half-time and I was still quietly confident we could get something out of the game," said Taylor.
"The character the players showed in the second half, not just getting two goals but carrying on after Stevenage scored again, was good.
"The supporters want to see brave players and we were. The penalty so early in the second half gave us a good start and it knocked the other team. We're delighted to get three goals, I don't care who gets them, as long as we do.
"I've never questioned the players' effort but on Saturday (in the 1-0 defeat to Oldham) there were times we could have done more.
"Here we were back at it, they were first class. Some of our performances have shown weaknesses and we've got to be stronger than that. We've shown we're very capable."
- Sports & Recreation
- Danny Kedwell