The visitors had gotten off to a dream start thanks to Anthony Grant's terrific strike in only the fourth minute and went on to boss the opening half-hour of the match.
They created several openings during this time and were made to regret not taking them as Wycombe grew in confidence after equalising through Paris Cowan-Hall.
The two teams will now meet again at Gresty Road in 10 days time and Crewe will be looking for a similar outcome to last season, when they hammered their opponents 4-1 in the same competition.
Davis said: "We're still in the draw and we've got to be happy because of that but we had a lot of chances and if we had taken some of those we could have been 3-0 or 4-0 up before half-time.
"But we haven't and they ended up scoring on the back of one of our attacks. I'm disappointed we haven't scored more goals and I'm also disappointed with the goal we conceded.
"Generally I thought it was a tie that was quite open, particularly in the second half when it was attack after attack from each side. In the end we're disappointed that we didn't get the win here but we have another opportunity at home."
Even before Crewe went ahead, Chuks Aneke had sent a header wide and they made Wycombe goalkeeper Matt Ingram earn his wages on more than one occasion whilst in front.
But all too often, big chances were sent high and wide, leaving Davis frustrated that what went on at the training ground is not being replicated on the pitch.
He said: "All we've done this week is shooting, of all different varieties, so you'd think after all of that it would be transferred to games.
"A lot of the shooting that we did was similar to the ones we missed today so you've got to transfer it and get goals in the big moments of the game.
"We didn't and Chuks has headed wide and hit one over, Max (Clayton) has taken a little too long on shots and in the second half we've had good opportunities.
"So there was a lot of pressure and a lot of opportunities that we could have done better with.
"They've had a lot of possession in front of us, but they didn't get behind our back four too much.
"In the end their goal has come from a free cross coming in from their left-back and we didn't get pressure on it and it was one of those that was behind our back four and their lad's nipped in."
The hosts shaded the second half but Brad Inman still had the chance to steal it for the Railwaymen as he shot over in the 90th minute.