Liverpool struggled for cohesion, with Bordeaux exploiting the space behind Jordon Ibe at right wing-back, and lost their most experienced player, Kolo Toure, to a dead leg in the 28th minute.
But the Merseysiders dug in, with Rossiter particularly impressive in the middle of the park, and took the lead midway through the second half through an Adam Lallana goal on his return from injury that was cancelled out in the 81st minute by a drive from Bordeaux substitute Ferreira Jussie.
"You're obviously disappointed, but I was more satisfied and encouraged by the performance," Rodgers told reporters after the game.
"We had so many young players in the team -- and some of these players were playing their first games -- so I thought it was very encouraging.
"Coming away in European games is always tough to do, but with the lack of experience we had and a lot of the young players, I was delighted with that.
"But if you can't win, especially away from home in European games, it's important you get a point -- and we certainly at least deserved that."
Rodgers also praised how Rossiter and Pedro Chrivella, who replaced Toure, controlled the midfield in the second half.
"Jordan Rossiter and young Pedro gained more control as the game wore on," he said.
"They were able to combine better with other players. It's invaluable experience for them and I thought they acquitted themselves very well.
"You take those two and you look at Jordon Ibe who is only 19 on the side, Joe Gomez is 18, so there is great encouragement there for young players and the supporters when they see them giving that type of performance," the manager added.
(Reporting by Simon Jennings in Bengaluru; editing by Amlan Chakraborty)
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