The hosts suffered an away defeat to St Johnstone last weekend and then crashed out of the League Cup to Aberdeen.
And Motherwell almost let the points slip after Shaun Hutchinson was dismissed on a second yellow card on 87 minutes and Hibs came close one two occasions to equalising.
"I think we were hanging on," said McCall. "But I think after a really tough week, we got what we deserved and we got the three points.
"It was a big three points after a tough week. It's good character by the boys, we have to regroup for a tough game against Dundee United next week, but three of our back four look to be out.
"We didn't play particularly well in the first half but we had three or four gilt-edged chances to go two or three nil up and we didn't manage to put the ball in the net."
McCall admitted he had no complaints regarding Hutchinson's dismissal, and he feared a resulting free-kick from Liam Craig or Rowan Vine - taken by the latter - would prove costly.
"Not only was it a sending off, but I thought it was a penalty kick, which would have topped the week off," said McCall.
"But it is outside the box - it's the correct decision, and even then there was the feeling that Craig and Vine standing over the ball, they were both capable of putting it in the top corner, but thankfully the wall stood strong."