The Robins ended a painful three-game losing run against Challenge Cup foes Leigh Leopards last week and backed it up with a first win over Catalans in 10 attempts.
Three weeks on from their heartbreaking Wembley defeat, Rovers are up to fifth in Super League and on course for the play-offs.
"I'm really proud of the players and staff," said Peters.
"Catalans are a very, very good team and been the benchmark all season.
"What I'm pleased about is this week as well we were outplayed twice by Catalans and the players found a way again to turn it around.
"You've got to go through experiences to learn and we're getting our learnings and the good thing is we're doing something about it.
"The resilience shows our character. I'm really pleased for the players because that will give them a lot of belief."
Rovers hold a two-point advantage over top-six rivals Salford Red Devils after Paul Rowley's men went down 26-8 at new leaders Wigan Warriors.
The Robins host Salford in the penultimate round but Peters is not looking beyond next week's trip to Huddersfield Giants.
"We're heading in the right direction but we're not getting carried away," said the Rovers boss, whose side have won only one of their last six away games.
"We've got to go to Huddersfield and show we can do it away as well as our away record hasn't been the best and we need to look at why.
"But I'm confident within the group because when we've needed to fix something, we've found a way to fix it."