Lionel Messi scored a hat-trick, while Luis Suarez contributed with a brace to the scoreline as the Bhoys suffered their worst defeat in European club competition.
The visitors were awarded a penalty when the score was till 1-0, but Moussa Dembele's weak effort was saved by Marc-Andre ter Stegen, before Barca put the foot down and scored six goals through Messi, Suarez, Andres Iniesta and Neymar, who produced four assists.
Rodgers told BT Sport 3: "We put a huge effort into the weekend and got a fantastic victory.
"It's always going to be really, really tough in your next game to probably the best possession team in the world.
"I think in the first half we had a critical moment in the game. We went 1-0 down very early and then got a great chance and I think if you get the penalty and get it to 1-1 then it makes it a little bit nervy, especially after them losing at the weekend.
"But, of course, not long after that they got the second goal and I think in the second half we ran out of legs to be honest.
"The game at the weekend added to the immense quality they have in their game and it obviously becomes very difficult and then the scoreline by the end is bitterly disappointing.
"There's a lot to take from the game for the players in terms of technique, in terms of simplicity and quality and lots of things to learn for them from the game."