Moyes was particularly impressed with Arnautovic - whom he described as "unplayable" - but the Scot was impressed with his entire team who have concluded the season with seven points from three matches.
The 55-year-old is quoted by Sky Sports News as saying: "What a great performance. It was a good game, the players enjoyed it, I enjoyed watching it and we scored good goals.
"Our play all day was really good, in recent weeks our form has been really good, our football has improved, the players have got better, so that's good.
"Look at times [Arnautovic] can be unplayable. He had other opportunities, he was in on the keeper. When we came in we were in the bottom three and we've ended up in 13th so I would have taken that all day long, that's for sure."
Moyes is now out of contract at West Ham and talks over his future are expected to take place in the near future.