It was a fourth home draw of the competition for Arsenal, but their third against Barclays Premier League opposition.
Wenger believes that in itself shows how much dedication his squad have put into keeping alive a shot at a first trophy since 2005.
"People have questioned our desire to do well in the FA Cup many times, but we are in the semi-final now and from our performance on Saturday you can see we really want it," Wenger said.
"We took this competition seriously
Since the start of this competition it is true that we had a good draw in the fact that we played all the games at home, which is the first time (that this has happened) since I played in the FA Cup.
"But, on the other hand, we played difficult opponents - Tottenham, Liverpool, Everton and that shows you that we have taken this competition seriously."
Arsenal had taken an early lead through Mesut Ozil, the German's first goal in 15 appearances, but were pegged back before half-time when Romelu Lukaku tapped in following a surging counter-attack run by Everton's England World Cup hopeful Ross Barkley.
After Barkley had fired over when picked out at the edge of the Arsenal box by Lukaku on 54 minutes, the hosts eventually got themselves back in command of the tie when former Everton midfielder Mikel Arteta scored from a penalty, which was retaken following encroachment, after Gareth Barry had tripped Alex Oxlade-Chamberlain.
The match then opened up as Everton pressed to get themselves back in the game, which allowed Giroud, on after an hour for the ineffective Yaya Sanogo, to slot home a third on 83 minutes and then complete a fine flowing move to quickly make it four.
Wenger believes the manner of the victory can lift his side for what looks a 'mission impossible' in Germany next week, when they will be out to overturn a 2-0 lead by Bayern Munich in the second leg of their Champions League last-16 tie.
Pep Guardiola's side trashed Wolfsburg 6-1 away on Saturday to record 16th straight Bundesliga triumph, moving 23 points ahead of nearest rivals Borussia Dortmund with 10 games left.
Wenger, though, remains ever the optimist.
He said: "The win over Everton was the perfect platform to go into a game where the statistics go against you, but let's be inspired by our FA Cup performance and go to Bayern and try to repeat that.
"I am convinced we will have a real go."
Arsenal - without England midfielder Jack Wilshere for at least six weeks because of a broken foot - made a couple of changes against Everton, but should have defender Laurent Koscielny in the squad for Wednesday night after he missed out because of a hamstring problem.
Lukasz Fabianski will again be in goal, as fellow Pole Wojciech Szczesny is suspended following his red card in the first leg of the European tie.
Everton manager Roberto Martinez, meanwhile, will now regroup his squad for the Premier League run-in as they look to secure a top-six finish.
Leighton Baines captained the side with Phil Jagielka still out injured.
The England defender said on evertontv: "We are bitterly disappointed with the outcome because we came here with a positive frame of mind looking to win the game.
"We have got a couple of home games now (against Cardiff and Swansea) that we know we are capable of winning and know we probably must win in terms of having a push for the back end of the season with just the league to focus on.
"We want to finish strongly and those two games are hopefully the platform which we can build on."
Source : PA
Source: PA