Uruguay international Suarez bagged 31 Premier League goals last term as Liverpool finished second, just two points behind champions Manchester City.
Liverpool favourite Suarez was sold to Spanish giants Barcelona last month though, in a reported £75 million deal, leaving a significant void in the club's forward line.
The Anfield outfit clearly missed the striker in a scrappy 2-1 win over Southampton on Sunday and while Rodgers revealed that Suarez had sent the team a message of support before the match, the Liverpool boss is keen to move on.
"I think our ambitions here at Liverpool... they have to be bigger than one player. We've said that repeatedly," he said.
"Big clubs will lose players and our ambitions are bigger than Luis. He sent us a lovely text this morning, wishing us all the best and for his team-mates, and to start strong, which was a great gesture.
"He is a friend now of Liverpool. He's a good boy but he is gone. His heart is with Liverpool, he'll always be Liverpool and it was a lovely touch.
"[But] we look forward. We're bigger than any one single player.
"For us, I do still think we want another striker. That's something that we will look at but that will depend on the availability of one. So we'll search for that through to the end of the [transfer] window."
QPR striker Loic Remy almost joined Liverpool last month before reportedly failing a medical, while Paris Saint-Germain forward Edinson Cavani has also been linked a switch to Anfield.
