"When you lose guys like that you lose a big chunk of goals in your team," Lambert told a news conference ahead of Monday's league trip to West Ham.
"It's a big loss... for whatever reason he left the club. He's West Ham's player and we have to stop him.
Arnautovic provided the assist for striker Javier Hernandez as West Ham held Chelsea to a 1-1 draw last weekend.
"I don't know the guy personally but he had some good years here and scored a lot of goals, and assists as well. I saw him last week and he was very good."
Stoke are second from bottom in the league with 27 points from 33 games and Lambert said his team had to translate their positive performances on the pitch into results to avoid relegation to the Championship.
"If we get a win it drags a few back into the (relegation battle), that's the most important thing. If we keep playing the way we are and doing the things we've asked the players to do, we've got a great chance," the Scot added.
"You need a little bit of luck at certain times but the performances have been incredibly high. The way we've performed, I couldn't ask any more from the team."
($1 = 0.7028 pounds)
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Toby Davis)
