Gerrard will move to MLS side LA Galaxy at the end of the season amid suggestions Liverpool could have done more to keep him at the club.
The Reds skipper revealed earlier this week he would have signed a new deal had it been offered in pre-season.
But the offer of an extended contract did not materialise until November, by which time the 34-year-old was already considering his future.
That led to his decision to move on and Rodgers is now determined to draw a line under the matter.
Rodgers said: “There is nothing any more to add. Everything has been said on that situation that needs to be said.
“Steven spoke very openly and honestly with his feelings on it. When you see all the interviews you will find it was dealt with.
“His concentration is now on football. Now we really have to concentrate on the football and the team and keep the momentum going.”
The search is now on for a player to replace the club legend but Rodgers remains confident they will cope without Gerrard.
“There is no doubt Steven is still a top-class player and has been that world-class talent for many years,??? he added.
???Him leaving in the summer leaves a void on and off the pitch but the club has to keep moving forward. History shows players who have been great players here move on and it is an opportunity for other players to grab the mantle.
“I was fully aware part of the evolution of this group in the first two or three years (of his reign) was going to be that period where some of the great names of the club were going to move on.
“The likes of Carra (Jamie Carragher) in my first year were brilliant and come the end of that season he wanted to move on.
“It is very difficult for a manager, these are players who have been outstanding for the club. You have to have a plan in place to do everything you possibly can to replace that quality.
“That is a challenge for a manager in the model of how we work and we will have to work very hard to get that level of player in.
“We must also respect young players coming in need to be given that opportunity so hopefully they can become a star.”
Raheem Sterling is one such young player who has become a key figure at the club, with the England international expected to sign a new contract in the next month.
“Raheem has burst onto the scene and been outstanding and in one of the most competitive leagues in the world he has been one of the top-performing players,” said Rodgers.
“He still has a lot of years in his football education.”