Shire were well worth their win at Airdrie’s Penny Cars Stadium, dominating the opening stages before Dean Watson’s neat finish put them ahead on the half-hour mark.
As expected, Celtic came back into the game and created plenty of chances of their own, including a missed penalty, but the visiting goal remained unbreached.
Shire had further chances during the game to add to the scoring, with on-loan East Fife forward Jack Healy seeing his late effort saved by Celtic goalkeeper Ryan Mullen.
Shire held on for a deserved three points and now sit in a healthy seventh place.
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The young Celtic side are not accustomed to losing games of football, or even conceding goals, so Ure was understandably delighted with his side.
He said: “The players deserve all the plaudits after their performance on Friday night.
"Every single one of them.
"That’s what we asked from them before the game, we needed 11 people, plus the subs who came on, to play well and they all done that.
"Everyone did their bit which was really pleasing.
"It’s testament to them and they’ve set a standard that we know they’re capable of.
"That’s something we’ll reiterate to them that they must continue to meet that, starting with the next game against Stirling Uni, and then apply the same commitment, desire and hunger on Saturday and then every game, not just when they want.
"If you look at Celtic’s results that’s only the first or second time this season that they haven’t scored a goal which is pleasing.
"We had to ride our luck at times but the boys worked hard and deserved their victory.”
The game against Stirling Uni was scheduled to be played on Wednesday night as the Herald was being sent to press.
Likely to feature in the squad was new signing Olly Mcdonald who has joined the club on loan from Queen of the South.
"Olly is someone we were asked if we could bring in to take a look at,” added Ure.
"We have an injury in that department so a short-term loan deal suited all parties.”
It’s a busy spell for Shire who, following Wedensday night’s game, will welcome Edinburgh University to the Falkirk Stadium on Saturday.
Both sides may be sitting a few places below East Stirlingshire in the Lowland League, but Ure says it’s absolutely crucial his players go into these, and all, games with the correct attitude.
"We need to be at our best, Stirling Uni are always a difficult side to play against,” added the boss.
"If you look at Edinburgh Uni’s results recently, they’ve not been far away.
“Their result at East Kilbride on Saturday (Edinburgh won 3-2) was excellent.
"So we cannot take anybody in this league lightly.
"If we do, and we don’t apply ourselves properly like we did against Celtic, then we’ll come unstuck.”