Wenger feels the 26-year-old, who had marked his return to competitive action with a brace in the last round against Cardiff, has come back mentally stronger from his experience.
"It looked like a bit of a 'beach' goal - and he meant it, he sliced the ball," said the Arsenal manager.
"Eduardo is a surprising finisher and an intelligent player. He has short back lift and understands what to do very quickly.
"Goalscorers are moving in the box when everyone else is standing still, he has that.
"I have never seen him do that before, his goal was instinct and shows you that finishing is all about what you do in a fraction of a second."
Wenger added: "I did not expect him to come back like that, and it is a tribute to his personality. He has never complained and that is a big example in our world."
Another fine chipped finish from Mexican teenager Carlos Vela set Arsenal on their way on 25 minutes, with Emmanuel Eboue's late strike wrapping things up to book a home tie against Hull in the last eight.
The victory - achieved with several of the first-team regulars rested and which marked a welcome return for England winger Theo Walcott after four months out because of a shoulder problem - extended Arsenal's unbeaten run to 17 games in all competitions, and proved just the right tonic ahead of next week's crucial Champions League trip to Roma.
"We did the job in a serious way," said Wenger.
"The first half they made it very difficult because they marked us tight, but we scored brilliant goals and there could have been a few more.
"What is good before going to Roma is we did not concede and scored several goals."
Wenger hopes to also have captain Cesc Fabregas back from a serious knee injury in a couple of weeks, while Czech winger Tomas Rosicky could be another in action again soon following a long lay-off.
"We are going into the final sprint. For us it is important to keep all our targets alive," said Wenger, whose team have closed the gap on Aston Villa in the Premier League down to just three points.
"We know every game demands a big performance because we cannot slip up.
"Slowly, we have all of our players coming back, and that can be decisive."
Wenger added: "People judge always the instant situation. If you look now at the players who are still out - Fabregas, Rosicky and [Emmanuel] Adebayor - they can all contribute offensively a lot."
Burnley boss Owen Coyle, meanwhile, could certainly not be accused of instructing his men to sit back and take a beating.
In the end, though, the Coca-Cola Championship promotion-chasers just did not have enough about them to get a result.
"I wanted the team to be positive," he said. "People pay good money to watch football and we have an obligation to send out our teams to attack.
"We felt comfortable before the opening goal, which came from a mistake by one of our own players.
"However, the finishes were first class for their goals. I watched Eduardo's again on the TV, and it just seemed to get better and better. But you have to analyse it and understand the quality Arsenal have.
"Arsenal play with movement and pace at the very top level - which is why they are in the Champions League on a regular basis because they are a capable of doing that against anyone."
Burnley, who also reached the Carling Cup semi-finals, will now concentrate on forcing themselves back into the Championship play-offs.
Coyle said: "We have shown all season that we have good players
"We now have 10 cup finals to get promotion - if we can play to our level, then we can do well.
"If we have got anything about ourselves, we want to be in that division."