He played down talk of Chelsea contesting the title, despite winning their first two games of the season, saying his side needed to learn to keep up their tempo.
Morata was heavily linked with a move away from Stamford Bridge this summer, but he is confident that Maurizio Sarri's footballing philosophy will suit him better.
"For me, it's easy. I could have gone back to Spain or Italy, all the people believe in me there, but I want to change things here", he said.
"Last season it was direct balls and for me to protect the ball in the air and it's not my best quality".
"It was important that after three years of inconsistency in playing time in Madrid I've got into a team that wants me and a coach that wants and trust me. It's better for me".
The 59-year-old Italian, a heavy smoker unable to satisfy his habit on the touchline due to the smoking ban, was grateful for Eden Hazard setting up Marcos Alonso's 81st-minute victor. But, at the other moments, when we are not able to press in the other half, we are in trouble.
Sarri will no doubt work on Chelsea's defensive deficiencies in training this week and he also took the opportunity to announce another, more personal attempt at improvement.
"I have two years left on my contract and we'll see what happens".
On the touch-line, Sarri, wearing a baggy blue T-shirt and track-suit pants, waved his arms in frustration as he implored his players to close Arsenal down in their own half as the Gunners showed signs of fighting their way into the game.