The Gunners were undone by two goals in the space of three first half minutes, which effectively killed off the tie as a contest, leaving the home side needing to score four.
Arsenal, trailing 1-0 from the first leg, had started brightly, but the Emirates Stadium faithful were left stunned when Park Ji-sung capitalised on a slip by teenage full-back Kieran Gibbs to fire the defending champions ahead on eight minutes.
Wenger's side were 2-0 down following an audacious 40-yard free-kick from Cristiano Ronaldo. Portugal forward Ronaldo added a third on the counter-attack just after the hour before Robin van Persie scored from the penalty spot when Darren Fletcher was sent off - and so will miss the final - after being adjudged to have fouled Cesc Fabregas.
"It is the most disappointing of nights," said Wenger. "I felt the fans were really up for a big night and to disappoint the people who stand behind the team so much hurts really.
"We do not feel like we have played the semi-final of the Champions League because we were out of it after 10 minutes. The game was over before it started, that is most difficult to swallow. We can only look at ourselves I must say, but it's very, very disappointing to fight such a long way to get where we have been but to give the game away like we did."