However, Giggs believes United should have left Glasgow with maximum points.
"With so little time to go I suppose we'll settle for draw but with the way we played and our tempo in the second half, we probably deserved to win," Giggs told Sky Sports.
"It was a disappointing first half for us but the performance in the second half was much better. We came out and worked really hard and kept them pinned down.
"We knew chances would come. We knew we just had to keep the crosses and the one-twos going, keep the tempo up and it would come."