Michael Higdon and Chris Humphrey gave the visitors a 2-0 lead after just 10 minutes before Jon Daly pulled one back for the home side before half-time.
McCall's side survived a barrage of second half pressure to clinch all three points and gain revenge for their defeat to United earlier in the month.
"I think they'll probably feel a bit hard done to and that they deserved a point, similar to how we felt following the game they won at Fir Park," said McCall.
"We all know Dundee United are capable of fighting back and the goal before half-time gave them a lift.
"The second half we had to show a bit of grit and dig deep, we knew that we would have to defend well to get anything and with a young defence we did fantastically to get the win.
"It was a great bit of vision from Henrik Ojamaa to pick out Chris Humphrey and he took a good touch before producing a fantastic finish - it was a goal worth of winning any game."