The Villa manager watched his team, consisting of nine changes from the Barclays Premier League draw against Leicester at the weekend, toil against the Sky Bet League Two promotion hopefuls on Tuesday night before winning the third round replay 2-0 courtesy of late goals.
Wycombe had more than held their own against the much-changed, but still strong, Villa team and created the better chances before Ciaran Clark headed home with 15 minutes remaining.
Substitute Idrissa Gana sealed a fourth round home tie against Manchester City at the end of the month with a second goal in the final minute.
Asked if he was relieved, Garde said: "Yes, you can say that
But I think the result has taken a long time to come but it is fair
"We were disappointing for the first hour or so, technically poor
But then we started to play more collectively and simple and I am happy with the result
"T he team I started tonight had good players and we should have done better
We were the Premier League team tonight and I didn't see that
But everyone knows this type of game is sometimes a trap and we got the victory."
Villa came into the game buoyed by taking four points from the two Premier League games since the original tie at Adams Park 10 days ago
Garde wanted to maintain that modicum of momentum, acknowledging in the build-up to the match that last season's run to the final went hand in hand with Premier League survival - although any such repeat this time round would be nothing short of a miracle.
The Frenchman felt he had achieved what he wanted but also said he knew Villa must keep on improving.
"I think we have the momentum still, yes," he said.
"Four games unbeaten now is very good but we have done nothing and won nothing, of course
But from the situation we were in the past few weeks, I prefer this one now
"It is also important for the players to have scored two goals but we have to do better than tonight if we are to keep that momentum going."
Prior to Villa's goals, Wycombe created the better chances
Brad Guzan got down to his left to push away Sam Wood's first-time strike before a huge let off for Villa just before half-time as Guzan failed to collect Joe Jacobson's left wing cross and Garry Thompson sent his header over the crossbar
When the unmarked Thompson headed Wood's cross wide in the 61st minute it was followed by a chorus of boos from some disgruntled home supporters
Garde said: "I can understand the anger but it is the cup and it can be difficult
But we must improve, yes."
The Villa boss then praised Wycombe for their performances in the two games, adding: "I would like to congratulate Wycombe because they have played against us with a very good attitude and played very good football sometimes
"I want to congratulate them, and they should be disappointed tonight."
Wanderers boss Gareth Ainsworth was proud of his players' efforts
He said: "I'm disappointed we've been beaten but I'm extremely proud.
"They are a Premier League side with millions and millions of pounds worth on the pitch and for 70 minutes we more than matched them and in the first half we had the better chances too, but we ran out of steam I think in the end and the legs just went
"But I'm so proud to see that effort and belief and commitment that we could achieve something here tonight and we need to take that into our league now."
Source : PA