The Reds agreed a club-record £75million deal with Barcelona on Friday and the Uruguay international - currently serving a four-month worldwide ban from all football activities for biting Italy's Giorgio Chiellini at the World Cup - will travel to Spain for a medical next week.
Suarez scored 82 goals in 133 appearances and won the golden boot last season with 31 in 33 league matches and his departure leaves behind a huge void but Rodgers said filling it was not insurmountable.
"If there is one thing the history of this great club teaches us, it is that Liverpool FC is bigger than any individual," he said.
"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.
"We are focused on the future, as we strive to continue with the progress we have made and build on last season's excellent Barclays Premier League campaign.
"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."
Suarez asked fans to understand his decision to leave for Spain less than a year after agitating for a transfer to Arsenal.
"I hope you can all understand why I have made this decision," he said in a statement.
"This club did all they could to get me to stay but playing and living in Spain, where my wife's family live, is a lifelong dream and ambition. I believe now the timing is right.
"It is with a heavy heart that I leave Liverpool for a new life and new challenges in Spain.
"Both me and my family have fallen in love with this club and with the city but most of all I have fallen in love with the incredible fans.
"You have always supported me and we, as a family, will never forget it, we will always be Liverpool supporters.
"I am very proud I have played my part in helping to return Liverpool to the elite of the Premier League and in particular back into the Champions League.
"Thank you again for some great moments and memories. You'll Never Walk Alone."
Suarez left Anfield, however, with a reminder from Rodgers that while they were grateful for all he had done in his three-and-a-half years he should not forget that his improvement was linked with being at the club.
"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," he told liverpoolfc.com.
"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."
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