The former Swansea manager believes the Reds will continue to compete at the top of the Premier League as replacements for the Uruguay striker continue to be sought
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And former Swansea boss Rodgers is confident the Anfield outfit will recover from the sale of the 2013-14 Premier League's top goalscorer, though he did thank the forward for his contribution to the team's fortunes.
"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," a statement on the club's official website read.
"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.
"We are focused on the future. 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."