Rovers had the better of the first half, David Dunn seeing a shot deflect against the woodwork, before Tom Cairney's goalbound shot was brilliantly kept out by Royals 'keeper Alex McCarthy.
"I think we've had the better of the chances in the first half," Bowyer told Radio Rovers.
"I thought we dominated the first half and some of the football we played was excellent.
"Again we made the opposition change their formation, Reading changed to 4-3-3 to get in the game because of the dominance that we had.
"But again we are talking about the fact that we've had enough chances to win the game but we haven't, so that is the disappointment."
The visitors improved in the second half with Bowyer admitting that his side we very fortunate not to concede a penalty when Hanley appeared to bring down Chris Gunter in the box.
Instead the referee gave the decision Rovers' way, booking the Reading defender for simulation.
"I thought it was a penalty," added Bowyer. "I really did. But then a thought we had a good shout for a penalty ourselves when the lad isn't even looking at the ball and jumps into Jordan Rhodes.
"So I suppose you can say the ref has evened it up a little bit.
"Full credit to our lot in a sense that you see those games where they go down the other end and score and nick it 1-0, so I'm delighted with the clean sheet, but we just lack that composure in the final third.
"There are lots of positives to take from the game, but there's frustration that we've not won the game."
Rovers are back in action at Ewood Park next weekend when Leeds United are the visitors.
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