Messi, 22, scored all four as the Gunners lost 4-1 on the night and 6-3 on aggregate as the European champions marched on to a semi-final against Jose Mourinho's Inter Milan.
'Messi is the best player in the world by a large distance,' said Wenger. 'It is difficult because he's not always in the game, but when he gets on the ball he's really dangerous and unstoppable.
Centre of attention: Lionel Messi hit four incredible goals to destroy Arsenal
'When he changes direction at such pace no-one can stay with him. He is very young but he can achieve a lot. He has six or seven years in front of him touch wood that nothing happens to him and he can reach unbelievable levels.
'For example, the fourth goal he scored, I don't know many players in the world who can score that. He made the impossible possible. He has something exceptional.'Wenger was without five
first-choice players and bemoaned an opportunity wasted to add to Nicklas Bendtner's opener before Messi equalised but Abou Diaby picked a pass left to the Dane when a better option looked like a ball right to Theo Walcott.
VIDEO: Wenger on magic Messi.The Arsenal manager said: 'We started strongly and had a good opportunity to score the second goal. We had chances to come back to 2-1 but we missed a good opportunity.
'We made too many mistakes defensively to get away with it in a game like that. They were always first on the ball, in the space, and we were punished for that. We conceded cheap goals. They didn't have to work hard enough. When they have players like Messi, you can pay for any mistake.
'I must congratulate Barcelona. We lost against a team that is better than us. They are in the semi-finals and they have a chance to do it. They have players coming back and I believe they are the best side at the moment in Europe. But it's a cup. If we had taken every opportunity tonight, we could have made life very difficult for them.'
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Arsenal must lift themselves for the final five games of the Barclays Premier League, starting with a north London derby at Tottenham next week.
'Yes, of course, you worry,' said Wenger. 'It's a big disappointment and we have to recover quickly because we cannot drop any points to have a chance to fight for the Premier League.
'White Hart Lane has been a place where we've done well over the years, so we don't go there with a negative history. It forces you straight away to focus because you know it's going to be a derby.
'When you go out of the Champions League, the next day you are in front of a very empty future. Our dreams are involved in that but you have to address the disappointment and make sure you're ready for the next game.'
Gunned down: Arsenal players are despondent in defeat after Messi's heroics
Arsenal's players added their thoughts on Barcelona, Messi's performance in particular.
Goalkeeper Manuel Almunia said: 'They're brilliant. The team in general is fantastic. We played better in the first leg but Messi is very, very good.
'You have to try to anticipate what he's going to do but it's very difficult because he is so skilled. He can do whatever he wants at any time and it's difficult to stop this kind of player. He was great tonight. I have a very bad memory but I have to say he is the best player I have ever come up against.'
Bendtner added: 'He's a phenomenal player and he showed that again. They played some really good football. If you are going to lose, you want to lose by the other team playing you off the pitch. They were stronger than us.'
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