Despite taking the lead through Danish forward Nicklas Bendtner, Arsenal then conceded four goals as Messi ran riot to secure a 6-3 aggregate win for Barcelona and book their place in the last four of the Champions League.
After the game Wenger heaped praise on 22-year-old matchwinner telling Sky Sports: "For me, he is the best player in the world, and by a distance. When he's in the game, he's really dangerous. Once he's on the run with the ball, he's really dangerous.''
The Frenchman added: "I believe that we lost against a team that is better than us and have the best player in the world. Congratulations to Barcelona - they were better than us.''
While few defences in the world could have coped with Messi on the form he showed tonight, Wenger felt his side were the architects of their own downfall.
"Over two games, for a team like Arsenal, we conceded cheap goals. They didn't have to work hard enough,'' he said. "When you have players like Messi, any mistake you can play for it.''
Despite the one-sided scoreline, Wenger insisted his side could have fought their way back into the tie even after Messi completed his hat-trick. "We battled, we came back, we started well and at 3-1 we had chances to come back to 3-2,'' said Wenger.
"We missed a few opportunities where we could have been more dangerous.''
Arsenal goalkeeper Manuel Almunia, so impressive in the first leg, admitted he faced a torrid time in trying to repel the threat of Messi, who hit a hat-trick inside 21 first-half minutes before completing his tally two minutes from time.
"You try to anticipate what he is going to do but it is very difficult,'' the Spaniard said. "He can do whatever he wants and at any moment, and it's difficult to stop this kind of player.''
Bendtner also hailede Messi, and his team-mates: "They were the better team and sometimes you lose like that,'' the Denmark striker said. "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 today.''
Discussing Messi's individual performance, Bendtner added: "He's a phenomenal player and he showed that again tonight.''