Late goals from Raheem Sterling and Coutinho cancelled out Eidur Gudjohnsen's earlier opener for Bolton, who had Neil Danns sent off when they led 1-0.
And Rodgers lavished praise on Coutinho after the game, predicting the former Inter man to match Suarez's "world-class" talent in the years to come.
"You just pay money to watch that kid," he told reporters.
"Watch how he plays football. He can be a great role model for young British players who, for many years, may have been discarded because they didn’t have the stature. He’ll become world-class in the next few years.
"With Luis Suarez, he was at a level when he played in this team, and he grew with the model before getting into that world-class bracket.
"I can see Coutinho following in a similar sort of line. He may not be as prolific but he’s on his way to that level. He’s a wonderful player."
It was a nervy end for Liverpool, who were staring at an embarrassing exit, until an exquisite pass from Can after 86 minutes set up Sterling for the equaliser - and Rodgers singled out the summer signing.
He added: "He's a kid that’s going to go on and be a big player for this team and Germany. He can defend, pass, he’s quick, he’s powerful. A lot of these young players are standing up to be counted now."
Liverpool now travel to Crystal Palace on February 14 for a place in the FA Cup quarter-finals, with Rodgers noting the 3-1 Premier League loss at Selhurst Park in November.
"[Going back] is a great thing," he said. "We didn’t play anywhere near our level and that the lowest point of the season in terms of performance.
"We go back there very soon with a different frame of mind and level of performance. Alan has lifted the club since he’s gone there but we go with big confidence."
