But Arsenal manager could get into trouble for confronting referee and criticism of pitch.
Arsene Wenger proud of Arsenal despite Champions League exit
Trailing 4-0 from what the Arsenal manager labelled a "shocking performance" in the San Siro three weeks ago, it was always going to take something special to turn the tie around and progress to the quarter-finals.
For a while at the Emirates Stadium it appeared the record books would be torn up as the Gunners reduced the deficit with first-half goals from Laurent Koscielny, the impressive Tomas Rosicky and Robin van Persie's penalty.
However, the second-half onslaught never came as Milan – who had somehow managed to go out to Deportivo La Coruna in the 2003/04 quarter-finals having won 4-1 at home, losing the second leg in Spain 4-0 – regrouped and were not really troubled during the closing stages, with only a scuffed close-range effort from Van Persie to show for Arsenal's industry.
Wenger was nevertheless left incensed by what he viewed as gamesmanship by the Milan players, with 21 fouls awarded against his side by Slovakian referee Damir Skomina.
The Frenchman – who served a touchline ban at the start of this season's qualification stage for his outburst after the exit to Barcelona 12 months ago – is believed to have been involved in a heated exchange with the referee as they left the field.
Responding to a general question on the match officials in his post-match press conference, Wenger said: "I was not happy with the referee tonight because I felt he gave many free-kicks in the middle of the park.
"Every time they went down a free-kick was given for them, and they sensed that very quickly and they used it very well."
In the build-up to last night's game, Arsenal recorded morale-boosting victories over Tottenham and Liverpool.
Another rousing performance was just what Wenger had wanted, although it was missing the fairytale ending.
He said: "The players put in a faultless performance, with fantastic spirit and you can only congratulate the whole team. We were very close."
Wenger, however, was also still annoyed by the manner of their humiliation in Italy, which came on a playing surface which had been relaid just days before.
He said: "It is maybe an easy excuse, but I feel Uefa has a lot to answer for because if you arrive at 7.46pm you get fined, but you can play on a bad pitch and they don't say a word.
"I just feel it is part of the respect for people who pay their money and go to a football game and expect conditions where you can play football.
"That's what we try to do here and it is unacceptable for Uefa to accept pitches like the one in Milan."
Despite all of their courageous endeavour, Arsenal must now concentrate on retaining a place in the top four of the Barclays Premier League to make sure such engaging European nights return next season.
"For us every point is a battle and until the end of the season that is what is in front of us," Wenger said.
For Milan coach Massimiliano Allegri, the end product of qualification for the quarter-finals mattered more than being beaten.
He said: "We did not have the wrong approach and knew we were going to face a difficult match.
"We could have done better, but in the end we got the result and qualified."
Benfica 2 Zenit St Petersburg 0 (Benfica win 4-3 on aggregate)
Benfica produced a dynamic performance to overturn a first-leg deficit against Zenit St Petersburg and earn a place in the last eight.
The Portuguese team trailed 3-2 from the first match, which was played in freezing conditions at the Stadion Petrovskiy, with Roman Shirokov scoring his second goal of the night to win the game after Oscar Cardozo had levelled late on.
But they attacked the Russian outfit from the off tonight and, even when Maxi Pereira's goal in first-half injury-time put them on course to win on away goals, the Eagles pushed on until Nelson Oliveira secured the outright win in the 92nd minute.