United was gifted a goal in the 8th minute when the 19-year-old Gibbs slipping on the turf, allowing South Korean Park Ji-Sung to pounce on Cristiano Ronaldo's cross and give United the valuable away goal that meant Arsenal needed to respond with three goals to advance.
That margin quickly became four as three minutes later Ronaldo scored on a free kick from 40 yards inside Spaniard Manuel Almunia's near post.
"The game was over before it started," said Arsenal manager Arsene Wenger, who took off Gibbs at halftime and replaced him with Ivorian Emmanuel Eboue.
Wenger called the loss the most disappointing of his 14-year career with the Gunners.
"It was the most disappointing because I felt the fans were really up for a big night and to disappoint people who stand behind the team so much hurts," he said.
He acknowledged United was too much for his inexperienced team.
"Tonight we were caught by a team that has the art to kill and take advantage of every mistake you make," he said.
Fellow Frenchman Patrice Evra was more blunt.
"We are 11 men," said the United left back. "They are 11 children. This is the difference. We are much more mature and have more confidence."
May 5 in London
Arsenal 1 Manchester United 3. Goals: van Persie pen. 76; Park 8, Cristiano Ronaldo 11, 61.
Arsenal -- Almunia, Sagna, Toure, Djourou, Gibbs (Eboue 46), Walcott (Bendtner 63), Fabregas, Song, Nasri, van Persie (Vela 79), Adebayor.
Manchester United -- van der Sar, O'Shea, Ferdinand, Vidic, Evra (Rafael 65), Cristiano Ronaldo, Fletcher, Carrick, Anderson (Giggs 63), Park, Rooney (Berbatov 66).Red card: Manchester United -- Fletcher 75.
Referee: Roberto Rosetti (Italy).
(Manchester United wins 4-1 on aggregate.)