The East London side offered little in their 3-1 defeat to Newcastle at St James’ Park on Sunday (May 17).
West Ham will be relegated if 17th place Tottenham manage to beat Chelsea at Stamford Bridge on Tuesday, although a draw would effectively see them go down.
Speaking to BBC Sport after the game, West Ham captain Bowen admitted they haven’t given up hope just yet.
"The way we started was really poor. We were late to pressing them and they have the quality to play through us," he said.
"It's obviously (down to) us on the pitch. We knew what we wanted to do and the pressue we wanted to put on them. We just didn't do it well enough. We have to hold our hands up and admit we didn't get there in time.
"I don't think so (the players were affected by pressure of relegation). I think if that was the case we would have probably sat off.
“We knew we had to be on the front foot and disrupt the atmosphere they created but we didn't do that and conceded really poor goals.
"It's those little things that we need to be better at. Silly mistakes are going to get punished in this league."
On the relegation picture: "Things obviously don't look great, we have to accept that. We need Tottenham to lose on Tuesday night and until then we have to hold on to what we have.
"We are holding on by a small thread but we are still holding on. We have to see how the result goes on Tuesday, there's a chance that we are relegated then and we can't hide from it. The only thing we can do is wait and see what happens.
"I will watch it. We never want to be relying on teams but we have put ourselves in this position. We have created this mess and I think we have to be big enough to watch it and accept what happens.
“We are still holding on and hopefully if they lose it gives us a chance on the final day."