Britton left the Liberty Stadium to sign for Sheffield United in 2010, but Rodgers brought him back to the club in January 2011 before their promotion to the Premier League via the playoffs later that year.
And after what Britton described as a tough game against Rodgers' new side, he insisted he was pleased to see both the manager and former team-mate Joe Allen doing well.
"It's great to see him," Britton told Sky Sports. "Obviously I owe him a lot for bringing me back to the football club. It was good to see him and hopefully I'll see him after the game.
"It was good [to face Allen]. I know Joe well from him breaking through at the Swans and obviously we were delighted for him to get the move [to Liverpool], but it's tough. He's a very good player and it was good coming up against him."
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"It was a tough game out there, not too many chances," he added. "But we've come away with a point and we're happy with that.
"I think it was quite a tactical game. You could see it was two teams who like to pass the ball and try to find an opening. It was tough out there but we've come away with a draw.
"We're doing well. Obviously at the start of the season we've got new players, new management - it takes a bit of time to settle down but the new players are settling in well and we're on a good run of form at the moment."