Barca captain Lionel Messi scored a hat-trick and Luis Suarez a double with further goals from Neymar and substitute Andres Iniesta while Moussa Dembele had a penalty saved by Marc-Andre ter Stegen when it was 1-0 to the home side.
Rodgers, who had described Suarez, whom he worked with at Liverpool, as the best player in the world before the game, acknowledged the prowess of the Catalan giants who were on a different level to the Scottish champions.
He said: “This will be a brilliant learning season for us in the Champions League. Tonight is one of the tough nights that you take at this level.
“There can be no embarrassment because they do that to better teams than ourselves. Professionally it is never nice when it happens.
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“We gave away the goal early, but I thought we came back into the game and once we started to get a bit of belief and confidence to pass the ball we started to create opportunities.
“There was a massive moment in the first half.
“If you can get the penalty and get to 1-1 then it can make the crowd nervy especially after their loss at the weekend.
“To go down 2-0 quickly, was obviously disappointing.
“The combination of our tiredness and their quality and freshness - these are top-class players.
“The pitch is fantastic. The ball moves as if it is on an ice rink and they move as fast as that, they are high-level, top players with big belief and that is why they are what they are.”
Rodgers was not for blaming Dembele for failing with the penalty.
He said: “I think credit to the goalkeeper. Moussa was happy to accept the responsibility.”