The Brazilian playmaker landed heavily on his shoulder following a challenge from Swansea City defender Ashley Williams during the teams' 2-2 draw at the Liberty Stadium on September 16.
And he is now facing a spell of up to six weeks on the sidelines after going under the knife to correct an issue picked up as a result - though he is keen to make a quick return.
"It's annoying to get injured, especially when you are playing well, but that happens," he told Globo Esporte.
"I now want to focus on my recovery, and do everything right to be back as soon as possible to help Liverpool in the league.
"The surgery was a success and this is what matters the most. I'll be back soon."
Coutinho has been capped on just one occasion by Brazil, and accepts that he must perform domestically to return to international duty.
"I dream of getting called up again for the national team, but it's only up to me," he added.
"Of course it's bad when you get injured in a moment like this, but this is football.
"I have had a set-back and my concern is being fully ready as soon as possible. If I play well, things will happen naturally."
