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Arsenal failed to muster a single shot at Camp Nou as they were eliminated 4-3 on aggregate, the first time a team has failed to do so since Opta's Champions League records began in 2003.
While their goal came from a Sergio Busquets own goal, Lionel Messi scored twice - once with an exquisite chip and volley and once from the penalty spot - with Xavi himself also on target as Barcelona progressed to the quarter-finals of the Champions League.
Arsenal manager Arsene Wenger felt aggrieved at a second yellow card shown to Robin van Persie when he was adjudged to have kicked the ball away after referee Massimo Busacca whistled for offside, but Xavi felt the decision to dismiss the Dutchman was the correct one.
Barca's captain for the night was also surprised by the overly-cautious approach of an Arsenal side that won the first leg 2-1 thanks to some expert counter-attacking.
"This is a fair result," Xavi told the Barcelona official website. "We were the superior team both in the away game and at home. There's justice in football. They had clearly come here to defend. They didn't even have one single shot on goal. I expected a lot more from them to be honest.
"[Javier] Mascherano and [Sergio] Busquets are simply amazing for the team, while Leo [Messi] once again stepped up to make the difference. The only thing that could have been better was our finishing. We should have scored more and we suffered too much. We could have killed the game a lot sooner.
"Arsenal really didn't want to play football. All they cared about was defending. The red card did affect the game, but the decision was right in my opinion."