The 25-year-old, who joined the Catalan giants from Liverpool in a £142m deal last month, got off the mark on his fifth outing for the club.
Speaking to Gol TV at full time, the Brazilian said: "I feel happy to have scored my first goal for Barca and have helped the team get to the final. It's a special moment.
"My first goal for Liverpool was also set up by [Suarez]. I hope I can help him and Leo (Lionel Messi) to score goals, too. They have been great since I got here and they've helped me fit in from the start.
"I feel really happy because I have been looking for that first goal since I got here - and finally I've got it," Coutinho told after the game. More importantly, though, it was able to help the team reach the final. For me, it will be my first final [with Barca] and it's an important moment.
"It's a special thing to reach a final and I am sure it will be a great game, but also a difficult one, like all finals are. But we have time to prepare for it. Before then we have a lot of games, so that's where our focus is now."
Former Liverpool striker Suarez set up both of his side's goals on Thursday night.