The forward praised Xherdan Shaqiri for the role he played in creating the chance that won them the game.
The Austrian was on the score-sheet against the Blues as he scored the only goal of the game to secure all three points against Jose Mourinho’s side.
It was the second time that the Potters have beaten the reigning champions this season, having beaten them in the Capital One cup 10 days before their weekend win, and Arnautovic says they will look to build momentum from those two victories.
“It’s fantastic to win two games against Chelsea, but now we have to be positive and keep performing well, especially at home,” he told stokecityfc.com.
“We have forgotten about the disappointments at home now, but we also have to forge about the Chelsea games and concentrate on winning the games in front of us.”
Arnautovic was also keen to praise Xherdan Shaqiri for the role he played in helping to create the chance that gave Arnautovic the opportunity to score the winning goal in the game.
The Swiss international was the Potters’ big money signing in the summer, but has so far failed to find the kind of form that made Stoke so keen to secure him ahead of a number of suitors.
He was impressive against Chelsea though, with his direct running cause defender Baba Rahman problems all afternoon, and Arnautovic was full of praise for the Switzerland international.
“I thank God that I was able to score the goal, it meant a lot to me and I think the supporters saw that in my celebration,” he added.
“The ball from Shaqiri was superb, he was tremendous all game, and then Glen Johnson put the ball into the box, it came to me and I tried something, which went well. I am thankful for this.”