The Potters were trailing 1-0 to Daniel Sturridge's first-half opener when they were awarded a penalty as Daniel Agger inexplicably handled in the area.
But Walters saw his spot-kick superbly saved by new Reds goalkeeper Simon Mignolet, who was also back on his feet quickly to deny Kenwyne Jones' follow-up.
And Bowen, who stood in at the post-match press conference as new boss Mark Hughes had dashed off to scout a player somewhere in Europe said: "You're disappointed because you think you're going to come away with a point.
"He's missed a couple in the past but he struck it well enough. I just thought the keeper made a good save.
"Jon Walters gives everything for this club, so nobody in the dressing room will do anything other than pick him up and get him ready for the next game."
Bowen had praise for his own goalkeeper Asmir Begovic, who did more than enough to give the Potters a chance of snatching a point with a string of saves.
"I thought it was going to be a battle and the keeper (Asmir Begovic) kept us in it at times," he added.
"It was a case of staying in the game as long as you can because we are asking them to play a different kind of game and you hope they don't lose confidence, which I didn't think they did."