An early strike from St Mirren loanee Kieran Offord put Shire into dreamland, and they should have been well ahead before the interval.
However, goals from Nick Locke and Kieran Mitchell sealed the away sides place in the final next weekend after they dominated the second-half.
Ure said: “Over the course of the season we have been in positions like that were we have been in a position like that to go a couple of goals ahead and go out of sight.
“We have dominated matches but teams always have moments in games and we were punished today for not taking our chances.
“In the second-half we just didn’t turn up. I am so gutted for guys in the changing room more than anything because they deserved over the course of the season to reach a final.
“It is a hard learning curve for the young players we have here at the club because in that second-half I just felt the Bo’ness players wanted it that wee bit more.
“The desire they had coupled with the way they saw the match out and managed it got them deservedly through.”
Offord was just one of a number of attacking players who passed up great one-on-one chances to make it 2-0, and he says if Shire want to make cup finals they need to take more opportunities.
“Now we need to dust ourselves down and go again next season,” Ure said.
“The goal that Kieran scored was top class, it really was stunning and that is what he can do.
“It’s a finish that we expect from him but wouldn’t from another player.
“He missed a couple of chances but so did other players out there.
“If you want to get to finals and win trophies, you can’t miss those chances.”
With the season now completed for Shire, the boss says the side’s sixth-placed finish can be bettered if he keeps most of the current squad on.
He said: “I’ve made it no secret that I want to keep the nucleus of this squad together for next season.
“I have so much to work with and the talent we have is quite something for this level.
“The future of this club is sorted if we can keep most of these guys, so I will sit down with the board and make that happen.”