The visitors quickly raced into a 10-0 lead at Rugby HQ, but the deficit was reduced to just three by half time and England went on to score 23 unanswered points to pick up a comfortable victory.
Hartley acknowledged that the start was not good enough, but was pleased with how they managed to turn the game around.
"[It was a] slow start from us today, I think Wales came out of the blocks, put us under the pump a bit and we got caught napping," he told Sky Sports News.
"Credit to the boys, they stuck in there and we got the win in the end. The first 20 minutes of that game we probably weren't quite up to where we needed to be. Full credit to the guys, digging in and getting that result."
England will now turn their attention to their summer tour of Australia, with their first match against the Wallabies coming on June 11.