The Merseyside club have claimed just one win, which came against Championship side Bournemouth in the League Cup, in their last five games in all competitions and sit 10th in the Premier League.
Liverpool's form is in stark contrast to that of last season, which saw them top of the table at Christmas.
However, the Anfield club did display great spirit as Martin Skrtel headed home an equaliser in the seventh minute of injury time to earn a 2-2 draw with Arsenal last Sunday.
Rodgers feels morale in the camp is on the rise but has challenged his side to turn their recent displays of character into victories.
"I would never question the character of this team. Slowly our game is coming back together," Rodgers said.
"The games versus Bournemouth and Arsenal you can see the confidence. You don't play as well as that if you don't have the confidence.
"We were disappointed with the result [against Arsenal] as we merited a win but we have to put a run of victories together to rubber-stamp our work."
Liverpool visit Burnley on Boxing Day before home games with Swansea City and Leicester City.
And Rodgers thinks an attacking style of play is the best way for Liverpool to be successful in those games and turn their fortunes around.
"We're at our best when our game is aggressive," Rodgers added.
"We've had to adapt this year. We had to steady the ship [after the 3-1 defeat to Crystal Palace last month] and had to get results but that wasn't long-term. It was about rediscovering tempo and intensity and we've seen that.
"That real aggressive pressure gives us the platform to dominate the ball so it's been a lot of work, we haven't just stumbled across this system, a lot of thinking time and hours have gone in on how we can maximise it.
"In the last three games it's been much closer, we have to work very hard, players are adapting to the club and performances will get better and better."
