In an interview last week the Uruguay striker said, unlike during a disruptive summer last year when he tried to engineer a move, he was settled at the club.
Securing Champions League football - in addition to signing a lucrative new contract in December - will have no doubt helped the 27-year-old's state of mind, and being named Professional Footballers' Association player of the year capped a remarkable turnaround in the last 12 months.
"Congratulations to him. It was an award that was really special for him because it came from his peers," Rodgers said of his 30-goal forward.
"He has been outstanding in all my time here and obviously, in particular, this season.
"So it was very well deserved and I know he really respected it, coming from the players in this country. I know he's happy.
"To know that he's happy is important, like it is with all of our players.
"It's very important that we have players here that are content, happy and focused on Liverpool."
Liverpool head to Crystal Palace on Monday night looking to maintain the pressure on title favourites Manchester City by getting the win which will take them top of the table again.
But, having come unstuck at home to Chelsea's defensive tactics just over a week ago, Rodgers is expecting a similar barrier at Selhurst Park.
"Every team in this league is a very tough game, home or away," the Reds boss added.
"I have been in this division a few seasons now and it is a very tough league.
"They have had some really good results at home. They will defend deep and play in a low block, the back four will be tight with the two wingers dropping in to make a six and the midfield three will be dropped in.
"They will look to break on the counter-attack and to stop us playing so we know it will be a difficult game, but that is our job to find that creativity and stay patient and make the breakthrough.
"Tony Pulis has done an outstanding job. Having come up with a team from the Championship I know first hand how difficult the job is.
"He has really galvanised the team. I watched them recently at Everton and they defended really well and have players on the counter-attack who can punish you.
"They have a real spirit amongst them, and keeping them in the league is a great effort."