Mbappe struck as Real won 4-2 on Sunday.
He told Real Madrid TV: "We played very well, we've been getting much better over the last few months. It's always difficult to play against Sevilla and we were a bit tired after the trip to Qatar. But we gave everything in the first half and we played very well right from the off. We scored some good goals and tried to play as a team in the opposition half. We scored a lot of goals and I think the Madrid fans will be delighted with today's performance, and so are we.
"I think we now know each other better. I've joined the team and that changed a lot of things. The settling-in period is over, as the coach says. I feel very comfortable in the team and I play better with the others on the pitch. The team is playing much better."
On his wonder goal, Mbappe also said: "The day before the game we take long-range shots and score some beauties. Today we scored another one. Valverde also scored another great goal. The third and fourth goals were also excellent because they were team goals. I think the fans enjoyed the goals today."
It was his 14th goal of the season and he added: “I can score a lot more, I know I have a lot more to give. The last few games I've played better, I took a lot of positives from the Bilbao game. I missed a penalty and I realised at that moment I have to give my all for this shirt and play with personality.”