Arsenal did so much to impress, but were ultimately their own worst enemy as they gifted the reigning European champions two late goals.
Arsenal will now have to recover quickly in mind and spirit to get a win at Manchester United this Sunday to keep their Premier League hopes alive because it is almost impossible to imagine them going further in Europe.
“It will be tough for us now but we will go there and try out hardest,” said Gunners midfielder Aaron Ramsey. “Against a side like that you have to take your chances.”
Messi scored in the 71st and 83rd minutes of a compelling tie which Barcelona deserved to win.
Arsenal had started so well, getting a sell out crowd on their feet by initially taking the game to Barcelona with precise confident passing.
But there was no end product and Barca slowly began to turn the screw, passing the ball patiently around the back trying to find a chink in Arsenal’s hard-working set-up.
By midway through the first half it was clear Arsenal would be doing all the chasing for the remainder of the match unless they could find a way to break up the metronomic passing game of the Catalans.
And that is just what they did on 21 minutes when Alex Oxlade-Chamberlain got his team on the attack and then forced a save from Marc-Andre ter Stegen after good work from Mesut Ozil and a shot from Hector Bellerin.
It was a poor connection form the boot of Oxlade-Chamberlain from what looked like a great chance.
Barcelona manager Luis Enrique, who guided his men to victory in the Champions League in his first season in charge, anxiously prowled the perimeter of his technical area, flapping his hands in exasperation as they looked to defend their crown.
It was not the look of a man top of La Liga by eight points and unbeaten in 32 matches in all competitions.
But there was a warning for Arsenal just before the break as Barca’s star-studded attacking trio of Messi, Luis Suarez and Neymar combined to create their best opening. Suarez then headed wide from an even better opportunity with the last touch of a first half that Barcelona had dominated only rarely looking Arsenal uncomfortable right at the end.
The only surprise at the start of the second half was Oxlade-Chamberlain was still playing following a clattering from Mascherano in the 37th minute.
The England forward had been limping ever since and was ultimately replaced by Theo Walcott after hobbling through five minutes of the second half.
And Barcelona were looking much more dangerous now, with Cech saving well from Neymar.
That marked the visitors’ first shot on target, but there was a growing feeling it would not be their last.
Arsenal clearly were unsettled now, their passing grew ragged, most notably from Aaron Ramsey, and they were frustrated with some Barcelona play-acting and its handling by Turkish ref Cuneyt Cakir.
So it was against the run of play that Olivier Giroud got on the end of a Mesut Ozil cross to force a good save from ter Stegen and so nearly break the deadlock.
Arsenal were hanging on, but they were still making a game of it in the knowledge a goalless draw would be a good first leg result.
Wenger clearly sensed blood, though, and sent striker Danny Welbeck from the dugout to come on for Giroud with just under 20 minutes to go.
But Barcelona were ahead before Arsenal could even make the switch. Wenger’s men were guilty of getting too many forward and were severely punished by the world’s greatest strike force in the 71st minute.
Suarez and Neymar carved the already exposed Arsenal defence open and the Brazilian played it back for Messi to convert with a characteristically classy finish past Cech.
Now Welbeck did come on, but it was Barcelona who looked most likely to score next, Suarez guilty of an horrendous miss as he hit a post when it seemed easier to score.
Ramsey had a chance to equalise seconds later to keep the Arsenal fans invested and his weary team-mates on the ball going into the final ten minutes.
But it was Wenger’s next change that ultimately ended Arsenal’s interest in the Champions League this season as Mathieu Flamini replaced Francis Coquelin and fouled Messi to concede a penalty within a minute of coming on.
The Argentine sent Cech the wrong way from the spot to leave Arsenal needing a footballing miracle to progress when they go to the Nou Camp for round two three weeks from now.
Arsenal captain Per Mertesacker, who’s poor pass to Flamini put him under pressure to concede the penalty, said: “We had to score at one point here and that’s why we do not deserve anything. You will never keep them quiet for 90 minutes.”