Daniel Sturridge scored the only goal of the game on Saturday in the first half with a precise drive into the bottom corner.
Mark Hughes' side could have taken a point from the match when a penalty was awarded for a handball from Daniel Agger, but Ireland international Walters saw his spot-kick well saved by Simon Mignolet, before his follow-up effort was also turned away by the Belgium goalkeeper.
Bowen, however, refused to lay the blame at the striker's feet, telling reporters: "Obviously we're disappointed because at that late stage you get a penalty and think you're going to come away with a point."
"He's [Walters] missed a couple in the past, from where I was sat he struck it well enough, I thought the keeper made a good save.
"Jonathan Walters gives everything for this club week in week out. We will pick him up and pat him on the back."
Despite the loss, Bowen hailed his side's efforts at Anfield, and was impressed by the way the team adapted to a new method of football under Hughes.
He also reserved praise for goalkeeper Asmir Begovic after the Bosnian pulled off a string of superb saves to keep the scoreline narrow.
"You come to Anfield and you expect a tough battle, our goalkeeper [Begovic] kept us in it a few times which you expect him to do because he's a top player," he added.
"It's a case of staying in the game as long as you can, we're asking this group of players to play a different style, and you have to make sure they don't lose confidence in that but I don't think they did."