Jake Beesley claimed a brace, as the Seasiders’ secured top spot in their EFL Trophy group.
The visitors produced some late pressure after a stoppage time goal from Farrend Rawson, but the home side were able to hold on.
"Sometimes it’s good to go through those nervy moments at the end of games, particularly with the players we had on the pitch,” Critchley said.
"I said to them, you’ve got to grind out a result sometimes.
"Other than them hitting the crossbar, I don’t think they really got near the goal or had a chance. We limited them.
"It’s almost like all bets are off near the end of the game, they just threw caution to the wind.
"I was really proud of the players because it’s not easy when you’re making 11 changes and throwing a team together against a team that has come full strength and is doing well in League Two.
"The boys really had to stand up to that.
"We had a young team out right at the end, and I was delighted that they got the victory they deserved.
"I love this competition. Morecambe brought their full strength team and we were a bit more experimental, so what a great challenge it was for our players.
"This gives us a chance to keep building on who we are as a collective- we still looked like a Blackpool team in the way we played, which is testament to the work done with them during the week.
"I’m delighted we’re in the next round. It starts to get more interesting now, and with the squad we’ve got, we can be competitive, and hopefully we can go far.”
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A downside from the evening for the Seasiders was an injury to Tayt Trusty, who was forced off on a stretcher during the second half.
"I’ve been to see him,” Critchley added.
"He’s got his leg in a boot- his ankle is quite swollen.
"You normally have to give these things 48 hours before you go to investigate a bit further.
"He wasn’t in great pain, which is a good sign, and he was smiling and talking, so hopefully it’s not too serious.”