Critics had rounded on Barca and their coach Gerardo Martino after the reigning champions suffered three defeats in six Primera Division matches, with the latest - a shock 1-0 reverse at lowly Real Valladolid on Saturday - seeing them fall four points behind arch rivals Real Madrid in the title race.
That loss came four days before Barca's Champions League last-16 second leg against City and would have given the English side increased hope they might be able to overturn their 2-0 deficit from the home leg.
However, there would be no fairytale recovery from City as Barca earned a 2-1 win on the night to progress through to the last eight 4-1 on aggregate.
And Messi, who was on the scoresheet along with Dani Alves - the same scorers as in the first leg, believes his side showed just what they are made of in Wednesday's match.
He said: "We were coming off two very serious setbacks away from home (at Real Sociedad and Valladolid), but more so for the performances than for the results.
"Here we've returned to be the Barcelona that we want, that the fans expect."
Messi also rubbished suggestions Barca's Primera Division title hopes have been sunk by their recent poor form, pointing out there are still 11 games to go - including a clash with leaders Madrid.
"I don't know if the criticism was exaggerated or not. We're the first to be self-critical and we know we haven't done things well, we know when we've done badly," said the Argentina ace, whose side are also through to the Copa del Rey final.
"We lost the opportunity to continue being close to Real Madrid, but the league isn't lost whatsoever. There's a long way to go."
Barca defender Alves echoed those thoughts, saying on his club's official website: "We're very happy to go on to the next round. When things aren't going well it's normal for there to be criticisms.
"Besides the goal I'm happy with how the team played, we always respond. There's only one path to follow. We had a slip, but we're moving forward."