The Croatian made his loan move from Real Madrid permanent this summer.
And Kovacic says Lampard has granted him more freedom than predecessor Maurizio Sarri.
"I am a Chelsea player now so I feel better about that," Kovacic said. "Last year was only a loan. I feel better and more confident than last year. It makes me feel more relaxed as last year was difficult and I needed to prove myself.
"Last year was also good, not perfect. This year I started well and I hope to continue like that. I am missing some part of my game and I can improve and get better, but I think it will come for sure.
"Lampard gives me more freedom and I can take the ball and go forward. I feel good. I have a good connection with the coach and all the team. We can change positions. We are aggressive. We are doing well but it is only one month with the coach so we can improve.
"Last season was also a good connection with the coach. It was also a good year last year. The connection is good [with Lampard]. The fans love him and so do the players. He is young and he understands us. We have a good connection with the coach.
"I feel better and more confident than last year. It is really important [that we got the result] because I think we started very well, in terms of playing. The results were not perfect but we played well. Today, we needed the three points more than a beautiful game. We did well and we won. Everything was perfect."