Suarez joined the Catalan giants on a five-year deal on Friday after weeks of speculation surrounding his future in the Premier League.
Liverpool's player of the year last season, Suarez began his campaign in September after serving a ban for biting Chelsea's Branislav Ivanovic and went on to score 31 goals in 33 league outings, firing the club to second in the top flight.
However, a third career biting controversy, while playing for Uruguay at the FIFA World Cup, will see Suarez miss the first four months of next term, with Anfield chiefs reportedly keen to move him on.
That coupled with Barcelona's pursuit has seen the 27-year-old make the move and Rodgers was keen to stress that he had done all he could to keep the star striker content on Merseyside.
He said: "Luis is a very special talent and I thank him for the role he has played in the team in the past two years, during my time at Liverpool.
"I think he would be the first to accept he has improved as a player over that period, along with the team and has benefited from being here, as we have benefited from him.
"The club have done all they can over a sustained period of time to try to keep Luis at Liverpool.
"It is with great reluctance and following lengthy discussions we have eventually agreed to his wishes to move to Spain for new experiences and challenges.
"We wish him and his young family well; we will always consider them to be friends."
Liverpool reportedly missed out on Alexis Sanchez as they look to replace Suarez - the Chile man joining Arsenal on Thursday - but Rodgers is confident suitable reinforcements will be sourced.
"We are focused on the future," he explained. "As we strive to continue with the progress we have made and build on last season's excellent Premier League campaign.
"I am confident we will improve the team further and will be stronger for this coming season, when we will be competing on all fronts; domestically and in the greatest club competition in the world, the Champions League.
"If there is one thing the history of this great club teaches us, it is that Liverpool FC is bigger than any individual.
"I hope our supporters continue to dream and believe that we are moving forward and with continued improvement and progression, together we will bring the success we all crave and deserve."
