United became just the second team this season to take points from the league leaders thanks to a 2-2 draw.
The odds may have been stacked against Cockburn’s side, who are battling to get away from the bottom end of the division, but they proved more than a match for the title favourites.
The United gaffer was delighted with his team and now wants them to carry the momentum of that performance into this weekend’s home match against Ormiston, a side who sit one place below them in the East of Scotland Football League’s First Division Conference A.
Cockburn said: “We said to the players before the game that we’ve been on a journey.
"We have a squad assembled now but we have to start finding the consistency level and get points on the board.
"We set a challenge between now and Christmas with the four games remaining and, on Saturday, we put in a very impressive performance against a good team who will probably go on and win the league.
“We went down there with a plan and the boys stuck to it.
“We told them to play without fear because we’ve been playing good football.”
Cockburn has been active in the transfer market since arriving at Saints and, on Saturday, had five of his new recruits on the field.
He believes their influence can continue to have a positive impact on the club over the coming months.
"We noticed a massive difference with the experience and the composure we had at the back,” added the manager.
"That breeds confidence throughout the rest of the team.”
Saints will now aim to make the most of their home advantage this Saturday when they look to kick some daylight between themselves and the bottom two clubs by beating Ormiston.
Cockburn added: “This is a tougher game than the Haddington one because we’re expected to go out at home and deliver.
"We’ve been asking the boys for consistency and if you can go to Haddington and come back with a point, at home we should be looking to establish ourselves.”
Kick off on Saturday is scheduled for 1.30pm.