Southampton had secured their survival last weekend, and their lacklustre performance came as no shock to manager Ralph Hasenhuttl.
West Ham boss Manuel Pellegrini has warned Marko Arnautovic to knuckle down and focus on football next season.
Arnautovic scored his first goals since January as the Hammers swept aside Southampton 3-0 in their final home game of the season.
“It’s not a coincidence that after some intense weeks and months, using that energy to stay in the league, and then you have a game today where you make a big mistake and go 1-0 down, that the physical energy is not so high,” said Hasenhuttl.
“That’s not a surprise to me. The power and conviction was not there. We have invested a lot. You could feel we were not that compact and a few steps too late.
“After the second goal the game was gone. That was the knockout. I know if you give Arnautovic space he is very clinical. The first goal is perfect for him, we made it too easy for him.”