PSG, who were without the suspended Marco Verratti and Zlatan Ibrahimovic, also had to make do with the absence of the injured Thiago Motta in Wednesday's match.
Without them, PSG failed to combine as a team, leaving coach Laurent Blanc to contemplate what his side lacked.
"Barcelona showed the style I love and appreciate a lot... it's been the same for 100 years now: have the ball at your feet and make the opposition run," he said.
Blanc, however, refused to make excuses, saying: "I do not want to talk about what could have happened with other players on the pitch."
But even if Verratti's absence was felt in the midfield, PSG were entirely outclassed by Barca.
Last month, Ibrahimovic did not help PSG much as he did not play in the first leg and was sent off after 31 minutes in the second as his team eliminated Chelsea on away goals.
They were also without Motta against the Premier League club in the first leg, which ended in a 1-1 draw.
Though he did not literally concede PSG were out of the Champions League before Tuesday's second leg at the Camp Nou, Blanc admitted he was at a loss.
Asked how his team could bounce back and overturn the two-goal deficit, he said: "If you have ideas, I'm taking them."
Defender Marquinhos also admitted that the missing players were not the reason for PSG's failure.
"We did not lose because we were missing players, but because of little collective mistakes," he said.
PSG did not press high enough and failed to cut Messi's feed, allowing the Argentine to collect the ball and have plenty of time to accelerate and set up Neymar for the opener in the 18th minute.
"They were collectively limited," former Olympique Lyonnais coach Remi Garde told sports daily L'Equipe.
"We can say it: collectively, PSG were not here, I don't know why. We would have liked to see the PSG who knocked Chelsea out but we did not see them."
PSG also lacked efficiency, with Edinson Cavani once again being blamed for missing several chances, while his Uruguay team mate Luis Suarez netted a double for Barcelona.
"Suarez was more efficient but he was playing in a team who was dominating, it was easier for him," said Blanc.
(Editing by Sudipto Ganguly)
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