The Tannadice side's commitment had been called into question following Sunday’s 9-0 defeat against Celtic that cost Jack Ross his job.
But Fox, who has been handed the reins as caretaker manager, oversaw a much-improved performance that saw the visitors hold on for a 2-1 win to secure a last eight trip to Kilmarnock.
Livingston manager David Martindale complained his side had been “bullied” by a United team with plenty to prove. “They didn’t outplay us, they did a job on us,” he said.
Fox was happy with that assessment. “I asked them for a reaction off the back of a period of poor results, culminating in Jack losing his job,” he said.
“Their personal pride has been called into question and we needed a response. I think they answered that. But it’s only one step on the way to hopefully getting back to where the club wants, and needs, to be.
“This cannot just be a flash in the pan. That was the last thing I said to them in the dressing room.
“They’ll get credit on the back of tonight and we are through to the next round — which is great — but we’ve now got a difficult game on Saturday away to Motherwell and we need to build on this.”
“All we can try to do, as a staff and a group of players, for as long as I’m here — that could be a day, a week, or longer, who knows? — is to repay some of those poor results and move forward.“The players have taken flak. I hope they are feeling better about themselves tonight. But it’s only a start.”
Fox recalled the experienced Charlie Mulgrew and Tony Watt and kept faith with ‘keeper Carljohan Eriksson.
“That was a decision I came to because I thought we needed our most experienced team on the pitch,” he said. “And I think I got a decent response from them. The players won the game, not the coaches.”