The visitors took the lead through Juhani Ojala’s own goal in the fourth minute, but confusion between Brad Jones and Jose Enrique allowed Raphael Nuzzolo to equalise.
Liverpool’s 19-year-old right-back Andre Wisdom headed Rodgers’ side back in front before half-time, but a quick-fire double from Young Boys handed the Swiss side a 3-2 advantage.
Sebastian Coates’ header in the 67th minute restored parity, before subsitute Jonjo Shelvey scored an impressive brace in a 20-minute cameo to help Liverpool to victory in Berne.
“I’ve got to give credit to the players, I thought they were absolutely magnificent. We had a very, very young side,” said Rodgers.
“I thought the boys were brilliant. It was a really tough game for us. The biggest thing we showed tonight, alongside our quality, was our character.
“We’ve got a lot of young players within the group but to come from behind away from home in a European game makes me really proud. We ran out very good winners of the game and it was a fantastic game to be involved in.”
Rodgers was particularly impressed by Liverpool debutant Wisdom after a composed display at right-back, while Spanish youngster Suso also caught the manager’s eye.
“I thought all the young players that came in were absolutely fantastic, the likes of Andre getting his first game,” Rodgers added.
“You can see he’s quick, he’s strong and he’s good in the opponent’s box, scored a terrific goal.
“I thought young Suso was outstanding as well, a real talent and the type of player I like. He’s exciting and once he adds goals to his game he’s going to be outstanding.”