Lavia enjoyed 45 minutes in Chelsea's 2-0 win against LAFC.
"Even before arriving here, we understood how big this competition was. We’re happy to be here," he told the club's website afterwards.
"It's great to see. We've watched some of the other games on TV as well. They are all great games and at a good level.
"I think every team has got different qualities because they're coming from a different environment. So it's nice to watch because you don't get to see all these teams often.
"We knew how good LAFC were and they showed that on the pitch. I wasn't surprised. I just thought they had a great team.
"As for my performance, for a first game it wasn't bad. I'm taking it game-by-game and will probably take the next few days to analyse the performance to get better feedback."
Fully fit
After a difficult past 18 months fitness-wise, Lavia played the first-half on the night.
"It was just about managing minutes," he explained. "There's no physical issue or anything. I feel very good, confident in my body and in what we can achieve as well.
"It's definitely something I'm aware of, so I do everything possible to stay fit. Honestly, the injuries I have had before, I just want to put them behind me and look forward to the future and feeling good."