The Austrian left Stoke for West Ham in a £25 million deal over the summer and was booed throughout on his return to the bet365 Stadium on Saturday.
The 28-year-old managed to silence the home crowd with West Ham's second goal on 75 minutes, and he felt his side's victory was thoroughly deserved.
"It was very hard for our supporters because they waited, first for the game to start and then for me to score," he told the club's official website.
"I had a few chances and I was disappointed for myself because I wanted to score the goal, but in the end when I scored the goal and I released the fans and the players and everyone with the club.
"It's just wonderful to get the win. It was perfect."
He added: "Obviously we played very well. The only thing Stoke had was the long ball. They are a threat with the long ball, but our back five did very, very well.
"The gaffer [David Moyes] wanted us to play football at the front and we did. I had a couple of chances and we could have scored at least five or six goals, but we got the 3-0 and we're very, very happy.
"We got the three points and we go again on Tuesday, when we go to Arsenal in the Carabao Cup and we want to get through to the next round."