Alex led 3-0 going into this Northern Final second leg and the Sky Blues looked to be heading out with a whimper until a Mark Ellis own goal and Leon Clarke strike - both in injury-time - set up a tense finish.
Davis said: "I'm full of mixed emotions. We gave them a lifeline out of nothing but it's about getting through to our first major final and that's what matters.
"We've taken this competition seriously from the start because we think it's a cup we can win. It's not been easy and this is our reward for taking this cup seriously.
"It's something to look forward to. We had a great time their last year and it will be a great experience for the players, fans and the town.
"I can't praise the players enough for this season. We have consolidated our place in League One and made a cup final, but I'm not going to write off a play-off push.
"Finishing halfway up the league isn't good enough for me and it won't be good enough for the players, we want to finish higher than that."