The Brazilian attacker made his full debut for the Merseyside outfit against Swansea at Anfield on Sunday afternoon and netted the second goal in an impressive 5-0 victory
The Brazilian netted in the first minute of the second half as the Merseysiders ran out 5-0 winners against the south Wales outfit at Anfield.
And Rodgers believes the 20-year-old attacker can get even better as he adapts to life in the Premier League.
"He’s a real talented player, Coutinho. He's only 20 but he's had good experience playing at a big level," the 40-year-old told reporters.
"He'll take a bit of time to adapt to the speed and the tempo, coming from Inter Milan his game is at a slower tempo. But he's a wonderful technician and you can see with his involvement in the first goal the quality and the speed of his passing, and he's got wonderful game knowledge as well.
"I've got high hopes for him. These are the types of players we're trying to get in - the technicians that have got strong character and mentality - and I'm sure he'll progress really well."
The Northern Irishman also underlined the importance of the win following a week in which the Reds suffered consecutive 2-0 defeats at the hands of West Brom and Zenit St Petersburg.
He continued: "It was an important three points. It's been a bumpy road this week in terms of the games Monday and Thursday.
"The Premier League is very important for us and we knew that we had to focus and show commitment today against a Swansea team that’s been brilliant this season.
"For us it was a very important win, an outstanding performance and I think we really showed our character and mental toughness today to get a performance like that.
"Funnily enough going into the game it was [all] about keeping a clean sheet, because the last four games defensively we haven't been at our best. Overall, we're very pleased and a very good performance."
Rodgers stopped short of claiming a late push for fourth is possible, however, insisting his side must stop plotting their own downfall.
"Every time I say [fourth is possible] you guys always write and slaughter me," he added. "I'm a manager, I'm an optimist but we're not getting carried away," he said.
"We've put in some outstanding performances this season and never always got the results. That's something we have to change for the remainder of the season and finish the season as strong as we possibly can."
Swansea coach Michael Laudrup, meanwhile, claimed his squad cannot blame the number of changes he made for their defeat.
"How do I explain it? It's a little difficult. Some could say 'you made a lot of changes', it's true. The first to blame is me, maybe, because I pick the team," he told reporters.
"[Liverpool] scored three goals in ten minutes - you cannot do that. We could have lost seven or eight nil easily if it wasn't for Michel [Vorm]. That's not good enough. But we have to learn from it, we have to go on and think about the final."