Taty Castellanos and Dino Mavropanos both scored twice for the win as West Ham swapped places with Tottenham and moved out of the bottom three.
Bowen, who missed a penalty in their FA Cup quarterfinal shootout defeat to Leeds last week, said: "A lot easier coming and speaking tonight on the end of a 4-0 win and out the relegation zone, we knew what was at stake before the game.
"It was a bit cagey the first half, a lot of nerves in the first half a game o this magnitude but there's highs and lows in games and it's about sticking together and showing our quality like we did in the second half.
"You play before everyone else around you plays. Everyone looks at results and your position. All you can do is focus on yourself. We're in a situation we don't want to be in but you have to face up to it and tonight was about facing up to it. We knew there would be difficult moments in the game but we're sat here now with a 4-0 win.
"I just try and put the ball in an area, he (Mavrapanos) has great timing. It wasn't pretty but as soon as I got half a yard I just wanted to put the ball in the box. The timing and leap he has got - the first goal always settles things.
"Games like this can be decided by set pieces. It's something we've been good at over the years and we have this season too.
"At half time I just said let's stay clam, there was a but of frustration, giving the ball away, a few mis-controls and it was a bit edgy, a bit nervy. Main message was to stick together as a team, we knew it will be a game where three points are vital, we're 45 mins from three points that would mean the world to us. We have to show our quality a bit more and we could've been better in the final third.
"There was opportunity to score more and really put a statement out there. But we've got a clean sheet as well and four goals."