Messi was in fine form throughout the game and opened the scoring in the first-half as the Catalan giants defeated Manuel Pellegrini's side in Camp Nou, winning 4-1 on aggregate.
Despite reaching the last-eight of club football's most prestigious competition, the Blaugrana have come under a lot of criticism as they have slipped four points behind league leaders Real Madrid in La Liga.
Speaking after the game, Messi said Barca deserved the victory against the Premier League club and feels his side's performance was of the level people have come to expect of them in recent years.
"We defeated a very difficult rival," he told Canal+. "After two very serious slip-ups [in the league] when we didn’t play well, today we saw the Barcelona that people expect to see.
“We played well throughout and achieved our objective of getting through.
“Despite their goal I don't think the tie was ever in danger [from our perspective]. Prior to my goal we were controlling the game and could have scored before.
“We knew we had to get a goal to calm ourselves down because of the potential they have."
Gerardo Martino's men have won only five of their last 10 games in La Liga but Messi is insistent that his side remain very much in the title race.
"We are the first to criticise ourselves. We know we did not do things like we should have, but that does not mean the league is lost because there is still a lot to play for."