“The teams around us are all playing each other and we still have a shot at climbing the table,” he said.
“Our goal is to finish as high as possible and I don’t think sixth is unachievable.”
Goals from Dylan McDonald, Connor Greene and David Churchill gave Shire all three points from a dominant display in the capital.
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Ure said: “It was a deserved three points for us.
“We started the match really well and we carried that on and should have really helped ourselves out by scoring a few more earlier on.
“We had to dig in for the the opening 10 minutes of the second half and we shouldn’t be having to do that. Letting opponents back in games has been one of our biggest downfalls this season.”
St Mirren loanee McDonald picked up his second man-of-the-match award in a row from a matchday social media poll, and Ure went along with that vote, saying: “He’s done brilliantly in the last two games and has contributed to our defence and attack in a big way.
“He’s a young player who gives his all in training, and on a matchday and he’s the type of loanee we want to have at the club.”
East Kilbride are Shire’s visitors at the Falkirk Stadium this coming Saturday afternoon, and Ure is hoping for payback after a narrow defeat in the last meeting between the sides in South Lanarkshire.
Despite Jamie Hamilton scoring early on at K-Park, Jack Stainrod netted a double to seal all three points for the hosts.
Ure said: “The match in November was one that sticks in your mind because we could have took something from the game. It was a frustrating one.
“They’re a side full of quality players and they are looking like the team most people expected from them now. It won’t be an easy game, but it is one we can win.
“If we want to reach the top six, it is matches like this we will need to take points from.”