Barcelona bounced back from their defeat to Atletico Madrid before the international break as further goals from Ansu Fati and Memphis Depay rendered Jose Gaya’s early opener for the visitors a mere consolation.
Coutinho, making his seventh appearance of the season, scored his first Barcelona goal since November 2020, after replacing Fati on the hour mark.
It has been a turbulent career in Catalonia for Coutinho since switching Liverpool for Barcelona in January 2018.
The 29-year-old has had to endure periods of poor form and fitness issues, and was sent out on loan to Bayern Munich in the 2019/2020 season to recapture his best form.
A move away from Barcelona was mooted in the summer but Koeman is adamant Coutinho can rediscover the spark that once marked him out as one of the best playmaker in Europe if he builds up his fitness.
"It was good," Koeman told reporters at his post-match press conference when asked about Coutinho's performance and impact following his introduction into the match.
"When he entered the game he was good. With his freedom we were able to control the game better. He knows how to score goals.
"He has taken an important step because I have always believed in Coutinho. Physically, he is getting better and better.
Coutinho has a contract with Barcelona until the summer of 2023.