United's first victory in eight matches was not pretty to watch on an uneven pitch and in gusty conditions but keen golfer McAllister was happy to quote one of Gary Player's favourite phrases: "The harder I practice, the luckier I get."
The Leeds boss added: "That is an adage I have used all through my career. These guys have been working really hard and deserved the little break they got here. When you've been out of football for a while and come back, there is nothing quite like winning a match.
"The conditions were difficult, it was really windy and the ball was bobbling, but I thought we did well. It was a one-nil grinder."
After a goal drought spanning 18 appearances, Tresor Kandol has now scored in United's last two games and his header was enough to land the win that took the side's tally to 50 points, not counting the 15 deducted from the season's start.
With McAllister looking to reinforce his strikeforce, Kandol's return to scoring form could hardly be better timed. Bradley Johnson's corner was cleared to David Prutton and his long cross was headed into the net by Kandol in the 25th minute.
McAllister said: "Goals are paramount for strikers' confidence. They thrive on scoring goals. We worked on getting the ball into the right areas for Tresor. It landed on his head and he produced a great finish."
Simon Cox should have equalised on 38 minutes but, from Christian Roberts' corner, he somehow headed over the bar from inside the six-yard box.
Casper Ankergren also made an excellent save to deny Roberts a late equaliser but United's keeper was rarely tested.
McAllister had to reorganise his side before a ball was kicked as Stephen O'Halloran, on loan from Aston Villa, was injured during the warm-up.
O'Halloran complained of pain at the back of his knee so Frazer Richardson took the Irish youngster's place at left back, with Alan Sheehan belatedly coming into the squad on the bench.
McAllister said: "Frazer had to come in at short notice and play in an unfamiliar position. He did a fantastic job."
Swindon's plans were also jolted when defender Kanyuka limped off with a groin injury with just 15 minutes gone, Jerel Ifil taking his place.
United's leading scorer Jermaine Beckford, back after serving a one-match suspension, missed a scoring opportunity after only ten minutes with a half-volley which cleared the bar but it did not matter as Kandol's goal lifted his team into eighth place, two points off the play-offs.