Jack Harrison rose at the back post to head home an 87th minute goal and give the Whites all three points, their fourth consecutive victory and top spot in the division.
The game was no classic, neither side creating a great deal of excitement for long, tedious periods of the game.
Marcelo Bielsa felt his team deserved to win it, Bowen felt it was a harsh way for the evening to end for his.
"It's tough to take," said the Reading manager, who set his side up to defend deep in numbers and attempt to spring away on the counter attack.
"We had a game plan. We did a lot of homework and preparation on Leeds and there a team that creates a lot of chances and dominates play.
"We had a game plan against them and the way I look back at it, yes, they had a bit of possession but I don't think our goalkeeper had a shot to save.
"That's a tick in one box. We spoke to the players downstairs and you're a little bit bitter because with our game plan we were obviously looking at playing a more counter attacking game but in doing that when we get a transition of play we've got to be better retaining the ball and do more with it in the final third of the field."
As bitter a pill as the late goal was to swallow, Bowen says there is little time for 18th placed Reading to feel sorry for themselves.
But he appeared to take some consolation from how little he believes there was to separate his team from the one who took the three points and sits in first place in the Championship.
"It's a mental thing for us now. We'll lick our wounds for 24 hours.
"You look at Leeds sitting at the top of the league. It shows the fine margins between any teams in this league. It's those little things you have to put right to give yourself a better chance at winning games."