The Hammers were beaten 2-1 by a late Villa winner scored via Jhon Duran.
New skipper Bowen said: "On another day, (our chances) go in and it’s a different story. The first goal was a gift. Lucas took his goal really well and we controlled the game a little bit more in the second half. We had some really good chances to go ahead in the game, but didn’t.
"This is the first game but there are 37 more. We need to go to Crystal Palace (next weekend) with the same fight, the same intensity.
"We got into some really good positions. At times we gave the ball away, at times we just didn’t put the ball in the net. You never want (to lose) the first game of the season, but we need to pick ourselves up before another tough game.
"With the spirit we have in the group, we knew we were fighting back. That was the penalty, and we gained more confidence with the goal. We felt we were in a really good position. On another day, we’d be standing here with a win.
"There are positives to take, for sure, but we’re in the results business. There are lots of positives and lots of things to work on going into our next game.
"We have exciting players. It’s an exciting time with a new manager and new ideas. There were signs that things are clicking and coming into play. Now it’s down to us to go out and show it."