The Austria international missed the Hammers' last three matches prior to the weekend because of a hamstring problem sustained in the 1-1 draw with Bournemouth on January 20.
"I was hungry before I got the injury," Arnautovic told reporters after the game. "My people helped me a lot to come back quickly. Nobody expected me to return that quickly. I try to give everything for the team.
"Watford kept the ball a lot because they needed to score but they didn't have a great chance you felt they had to score. Our counter-attacks and chances, we should have taken the game far away.
"I keep working hard on myself. It was a tough beginning to my time at West Ham. I wanted to prove the critical people wrong. I'm surprised some people don't like me as I have a good heart."
The result sees West Ham climb to 15th in the table, five points clear of the bottom three.