The 22-year-old received plenty of plaudits during pre-season, but has so far been unable to replicate that form in the early stages of the season.
Rodgers has confirmed that he initially wanted to give the midfielder a break, but due to injuries within his squad, was forced to play Coutinho in last Saturday's 1-0 defeat to Aston Villa.
"He's a brilliant young player, a fantastic young player," Rodgers said in this afternoon's press conference. "I've got no qualms about him - he's a big, big talent.
"He has lit up the Premier League since he came to the club. He's going to have some games where he won't be at his best, but he always gives his best and that's all I ever ask of the players. The kid is a great boy who wants to do well. He's very conscious that I have absolutely no doubts about him."
Coutinho was substituted in the second half of Liverpool's 2-1 win over Ludogorets Razgrad in their opening Champions League group game at Anfield on Tuesday.