Ryan Williams scored a late winner from a free kick to send the League Two side through to the second round of the competition.
"That's what football is all about. To win it late on with a well-taken free kick, that had the makings of a really good cup tie," he told Sky Sports News.
"We rode our luck at times but to go through to the next round is an unbelievable achievement. We have a lot of injuries and had a lot of our youth team on the bench tonight and players playing out of position.
"We were beaten on Saturday and I asked for response and we certainly got that."
Morecambe bounced back in the game following their opening day defeat to Wycombe Wanderers.