Messi was in inspirational form at the Nou Camp as Barca came from behind to progress to the semi-finals by wining 4-1 on the night and 6-3 on aggregate.
Nicklas Bendtner had stunned the Spanish giants with an 18th-minute opener to put Arsene Wenger’s Gunners ahead for the first time in the tie following a 2-2 first-leg draw at the Emirates Stadium.
But the Premier League side could not contain mesmerising Messi, who completed a stunning first-half hat-trick with a delightful lob before rounding things off late on.
Arsenal boss Wenger compared the Argentina forward – who was then aged 22 – to a computer creation.
“He’s like a PlayStation,” said the Frenchman. “I think he can take advantage of every mistake you make.
“Barcelona are a very good side but of course they have Messi who can make the difference at any moment in the game.
“He is very young but he can achieve a lot – there are not many players who can score four goals like he did.”
Barcelona suffered a semi-final defeat to Jose Mourinho’s Inter Milan, who went on to lift the trophy after beating Bayern Munich 2-0 in the final.
Seven-time Ballon d’Or winner Messi scored a record 672 goals in 778 games for Barca and lifted 35 trophies with the Catalan club before leaving last summer to join French giants Paris St Germain.