Randolph had saved a first-half penalty from former Well player Ross McCormack before Jamie Murphy gave the home side the lead with a fine finish to a good move.
He made several more good saves before he fumbled a corner from United substitute Max Gradel in the 67th minute which allowed the ball to fall at the feet of substitute Alex Bruce who swept the ball in to the net from close range.
Another United replacement, Ramon Nunez, scored the winner in the 74th minute to the cheers of the large travelling support.
However, McCall refused to point the finger of blame at Randolph.
He said: “It just slipped out of his gloves and it’s better to happen now than next week.
“You can count on the fingers of one hand, probably not even one hand, the individual mistakes he has made since he has been here.
“It’s an error and you move on. It’s not a big deal.
“He has been a terrific keeper for us and I’m sure that won’t affect him at all. It’s no big thing.”
McCall was pleased with his side’s performance in what was a competitive encounter but admits shooting practice will be on the agenda at training this week.
He said: “It was disappointing to lose the game because I don’t think we deserved to lose.
“We created a lot of chances against a Championship side.
“That’s what we can do. We have talked about that and the pace we have in the team.
“They have been our toughest opponents but we still created chances and it’s good that we did that.
“We just need to take a bigger ratio of chances.
“We had 14 attempts in goal against Partick in midweek which we could have done better with so it’s shooting boots on this week.”