Hakan Calhanoglu had opened the scoring for Milan, but the Italian side fell to a 5-1 aggregate defeat.
“We would certainly want to avoid Atletico Madrid,” said Wenger.
The draw for the quarter-finals – which features teams from eight countries – will take place on Friday at 12:00 GMT.This was Arsenal’s third win in a week after their first-leg victory in Milan and Sunday’s 3-0Premier League defeat of Watford.
Prior to victory at the San Siro, the Gunners had lost four successive games in all competitions.
“It’s much better. We needed that to recover from our results,” Wenger said.
“It shows how the team has responded. We had a difficult game but in the end we won it. If we have the results and the way to play football, the crowds will be behind us.”Turkish international Calhanoglu produced a stunning finish from 30 yards to give the Italians the lead.
The Gunners levelled within four minutes through Welbeck, who was controversially awarded a penalty after going down under minimal contact from Ricardo Rodriguez.
Xhaka’s long-range effort bobbled into the net for Arsenal’s second after poor goalkeeping by Milan’s highly rated Gianluigi Donnarumma, before Welbeck headed in a third.
“It was an open game. We played backwards a bit too much in the first half to protect the result. We played a very good side,” said Wenger.
“We have to improve defensively, but overall we are team with technical quality which is more attack-minded.
“We struggle a bit more when we have to defend. We finished the game more compact and more solid.”On the subject of Welbeck’s penalty, Wenger said he would “give an honest answer” after re-watching the incident, but AC Milan boss Gennaro Gattuso insisted it was not a spot-kick.
“In the same way a player can make a mistake, a referee can do a mistake,” he said.
“Even myself when I was a player, I would take advantage of individual situations. I’m not going to judge these things.”
Former England midfielder Jermaine Jenas, speaking on BT Sport, said: “It was a bad dive. It is cheating. Players like Dele Alli have been accused of that.
“It does tarnish the performance slightly. It was Wenger who said the English are getting better at diving; it was one of his own tonight.”
‘We can play against the top teams in Europe’
Victory means Arsenal will play in a first European quarter-final since 2010, when they were knocked out of the Champions League 6-3 on aggregate by Barcelona.
“We needed it. It was about getting the job done tonight and being professional,” said midfielder Jack Wilshere, who returns to the England squad for the forthcoming friendlies against the Netherlands and Italy.
“We didn’t start well but it woke us up. They got a good goal early on and made us work for it.”
Arsenal and Atletico Madrid are favourites to win the Europa League after Borussia Dortmund – previously tipped for the title – lost 2-1 on aggregate to Austrian side RB Salzburg.
“We are happy to be through to the next round and we will see who we get,” Wilshere added.
“When we looked at the draw before, AC Milan was probably not one of the teams we fancied but we showed we can play against the top teams in Europe.ConfusedGooner: Welbeck has ruined the match. His dive will overshadow our dominant performance over the two legs against AC Milan.
Loser92: I remember when AC Milan was a great team and could boast having the likes of Ruud Gullitt, Marco Van Basten and Frank Rijkaard among their ranks. How the mighty have fallen.
Alex: Starting to think we have a chance to lift the Europa League now. Hoping for Atletico Madrid in the next round, they’re the favourites, let’s get them earlier rather than the final.