Heads could have dropped having trailed 2-0 at the break, especially after the contentious penalty decision against them on the stroke of half-time, but Rovers rallied in the second half, reducing arrears thanks to Jordan Rhodes' spot-kick, but they just couldn't grab that all-important equaliser.
"Leicester is a difficult place to go and they are going to be right up there," said Bowyer after the game.
"We've said to out lads that we were pleased with the way they carried on in the second half and kept going, but we just weren't clinical enough in the attacking third and didn't really creating a great deal.
"But credit to them, they stuck at it and we've got to show that spirit more often. We had a go, we didn't come here to lay down and die."
The Rovers boss was also pleased with the impact that the substitutes made, particularly with Chris Taylor coming on and winning the penalty that Rhodes converted.
Bowyer added: "We've said to the lads all along that it is a squad game and I thought the substitutions on Saturday against Burnley showed that they can change the game a little bit and I thought tonights that the lads that came on affected the game."
Rovers now go again this Saturday looking to make it a hat-trick of home wins when Huddersfield Town are the visitors to Ewood Park.
Tickets are on open sale up until the 3pm kick-off, priced from £19 Adults, £12 Seniors and £7 Juniors. Book online today at www.onerovers.co.uk