The Seasiders had led for the majority of the game, with Jordan Rhodes marking his home debut with a goal in the fourth minute, before Josh Magennis equalised in the latter stages of the 90.
Well into stoppage time, Kenny Dougall scored a late winner to give the Tangerines their first league win since the opening day.
"I’m delighted with the result,” Critchley said.
"I think we deserved it with the chances that were created in the game- we showed tremendous character.
"We started really well with a fantastic goal. CJ (Hamilton) gets to the byline and Jordan (Rhodes) does what Jordan does- arrives at the last second, it was like now you see me, now you don’t.
"We were comfortable in the first half, and then we had chances after the break to kill the game off.
"The goalkeeper made some great saves and we didn’t quite see it out.
"It was a brilliant response to conceding. The three subs combined and made an impact.
"It was a great feeling for the players- and they deserved that.
"I’m made up for the supporters to celebrate a win and to see some goals, but I had no doubt that we would score.
"We’ve got to believe in who we are, and believe in the group. I think at the end of the season we could be a good team in the league.
"That win just settles everyone down a little bit. The players needed that to give themselves a bit of confidence.
"It’s a really good moment, a brilliant three points, but it wasn’t all bad last week and it’s not all good this week.
"I’m very proud, it showed the strength of character this group has got- which I never doubt,” he added.
"They always keep going- even with 10 men against Lincoln week.
"Are we going to get things wrong from time to time? Of course we will because it’s a new group, so we’re just trying to find who we are, and that takes it a little bit of time."