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Christian Pulisic opened the scoring with just five minutes on the clock, producing an assured finish after latching onto a clever Olivier Giroud flick.
The Blues continued to dominate proceedings until Pierre-Emerick Aubameyang's clever run just before the half-hour mark saw him sneak in behindAzpilicueta, who clumsily brought down the Gunners forwardin the box while trying to track back.
Referee Anthony Taylor pointed to the penalty spot andAubameyang stepped up to convert expertly from 12 yards, which saw the momentum of the match swing in Arsenal's favour.
Mikel Arteta's men pushed hardest for the winner, and were rewarded for their efforts whenAubameyang notched his second of the game in the 67th minute.
The Gabon international left Kurt Zouma with a delightful body swerve before dinking the ball over Willy Cabellero in the Chelsea net, sparking wild scenes of celebration in the Arsenal dugout.
Frank Lampard saw his side reducedto ten men when Mateo Kovacic was sent off for a second bookable offence moments later, and the Blues were ultimately unable to find an equaliser.
Azpilicueta questioned Taylor's decision-making post-match, but also admitted that Chelsea failed to maintain their usual high level throughout the entire 90 minutes.
"A lot of times there were 50/50s that went in Arsenal’s favour and we had the same in 2017 when Taylor also refereeda Chelsea-Arsenal final and gave Victor Moses a red card but we have to look further than this," the Blues captain told the club website.
"We have to look at ourselves. We know two weeks ago when we played against ManchesterUnited, we really controlled it. We played our game, we were on top of them against a very good side but today we couldn’t do it for 90 minutes and, in the end, that makes the difference."
Azpilicueta hadto be withdrawn ten minutes before the interval after tearing his hamstring, but he is already motivated to come back stronger and "learn" from the loss at Wembley.
"It’s my first time that it’s happened and it hurts a lot when that happens in a final like today,"said the Spanish defender. "Sometimes it’s football and it’s life but it’s hard to take.
"Now we have to learn from the game, even if you always want to learn when you win and when you lift trophies rather than by losing these kinds of games. It’s tough but we have the next challenges that we have to be ready for."
Azpilicueta added on where it went wrong for Chelsea against Arsenal: "It’s painful and a tough one to take. Obviously when you lose a final, it’s always painful.
"We started the game well and scored an early goal which normally gives the confidence to build on but we didn’t capitalise on it. We dropped our level a little bit and we were punished. When you score an early goal, you have control of the game. We had a couple of chances after that to make it 2-0.