The attacking midfielder scored his first goal since returning to LaLiga, netting the equalizer in Sunday's tough 1-1 home draw against Europa League winners Sevilla on Sunday.
Coutinho joined Barca from Liverpool in a reported €160million deal in January 2018 but struggled to assert himself in the first-team picture and was shipped out on loan to Bayern Munich last term.
At Bayern, Coutinho was part of the team that won a Bundesliga, DFB-Pokal and Champions League treble under Hansi Flick but the Bavarians opted not to make the move permanent.
Coutinho's future was shrouded in doubt, with Arsenal and Tottenham having been touted as potential suitors, but the arrival of Koeman afforded him a fresh opportunity at Barca.
It is one Coutinho is keen to take, with the Brazil playmaker saying in quotes reported by Marca: "I'm hungry to work and achieve big things.
"It was a tough and difficult game [but] we knew that already. It ended up being like that.
"We've got a point and now we're going into the international break. When we return, it's about continuing to work.
"We've had a difficult first three games, but we're just getting started. We're used to this and we'll keep working.
"Sevilla played very well. There were a lot of Sevilla players in the centre of midfield and that's why we struggled a bit. We have to correct that."
Coutinho celebrated his goal by tucking the ball under his shirt, as his wife is pregnant.
"My wife is pregnant and I wanted to dedicate my goal to her," he added. "It will be my third child."