Coutinho has impressed in pre-season and he was outstanding in Sunday's 4-0 win over Borussia Dortmund with a goal and an assist.
There will be extra responsibility on Coutinho this season, following Suarez's departure to Barcelona, but Rodgers is confident the Brazilian will rise to the occasion.
"He is so gifted as a player,” Rodgers said. “The supporters appreciated him against Dortmund because of the level of the opposition.
"His ability is magical in tight situations. He doesn’t get marked, tempts defenders out and his weight of passes.
"I just think he needs to add sustainability. He needs to do that on the big stage, and he’ll get that opportunity.”
Rodgers believes Coutinho will relish the opportunity of pitting his wits against the best players in the UEFA Champions League this season.
"He will show at that level he’s a top player," added Rodgers. "It’s about sustaining that level of performance and doing that on the big stage.
"I see him over the next few years being on the world level for Liverpool and Brazil."