Rodgers' side were beaten 2-1 in Greece by AEK Athens last night, going out of the Champions League 3-2 on aggregate.
The Ulsterman, who was replaced at Anfield by Jurgen Klopp in 2015, told BBC Scotland: "It's pretty obvious, you have to keep progressing and keep getting stronger.
“You only need to look at Liverpool, who got to the Champions League final and invested the money they had to be stronger.
“It's not rocket science. You have to always guard against becoming complacent and the way you do that is by adding to the squad. There are players we've kept, but obviously getting other players in.
“But that's for another day, there's a disappointment tonight from the players that were here that we let that slip through our hands."