Goals either side of halftime from John McGinn and Ollie Watkins strengthened Villa's push for Champions League qualification, but left the visitors rooted in the bottom three. West Ham are 18th with 29 points from 31 matches, their margin for error continuing to shrink.
In the relegation battle, Tottenham Hotspur, one point above the relegation zone in 17th, were thrashed 3-0 at home by fellow strugglers Nottingham Forest.
"Regardless of the result today, we have to focus on ourselves," Bowen told Sky Sports.
"We go into the break and then come back for a big end to the season. You have to hold your hands up and say they were better than us on the day - that's horrible to admit - but we just weren't at the races for whatever reason.
"We feel like we are still in a good place, we can't let this put down all the work we have done to get here. It has not been a good season at all for us, but we have to keep fighting to stay in the Premier League."
After the international break, West Ham host Leeds United in the FA Cup quarter-finals on April 5th before returning to Premier League duty in a pivotal clash against bottom-side Wolverhampton Wanderers on April 10th.
Watkins back with a bang
For Villa, Watkins' strike offered further encouragement after a challenging period. The striker was omitted from Thomas Tuchel's 35-man England squad for this month's World Cup warm-up friendlies following a dip in form.
The 30-year-old responded by netting his 10th goal in 43 games in all competitions this season.
"He is a fighter," Villa manager Unai Emery told the BBC. "He is always doing his tasks, and doing his tasks I am always delighted with him. Then it's numbers. Today he scored, but he must be consistent in his mentality to do his tasks and get his numbers.
"To be in the national team it is something every player wants but he must continue working and give the coach trouble (picking) for the next World Cup."