Saints built on last weekend’s thumping 6-0 victory over Ormiston with a 4-2 win away from home at Craigroyston on Saturday.
Things are trending in a positive direction for Saints, who are now up to 11th in the league table, but Cockburn says it’s important his side stays grounded.
"We're not getting carried away,” said the boss.
“It's two wins in a row and the first time the club has managed that since December 2019.
"It's nice and a good confidence boost but we need to keep going because we're still at the wrong end of the table.
"We weren't overly impressive in the first half but, after a word in their ear at half time, we came out and turned the game around.
"The whole squad did really well and it was impressive.
"We spoke in-house about setting targets and seeing where we could be at Christmas time.
“We're well on target to meet the objectives that the boys set themselves.
“The Christmas break will be a good incentive for the boys because they've put in a lot of hard work over the past few months.
“On the other hand, it's maybe come at the wrong time, given we're starting to get on a roll now.”
United this week host Edinburgh United and Cockburn wants to keep the run going.
"The boys are full of confidence and hopefully that bleeds into the performance on Saturday,” he added.