The Robins have taken 28 points from 19 games since the 49-year-old took charge, which have lifted the side up to 15th place in League One.
"Had you offered me that when I first walked through the door, I would have taken it," Cotterill told the Bristol Post.
"I had my sights set on taking 30 points from 19, because that would have been double what they got from the same number of games at the start of the season. But we couldn't get the wins we should have had against Swindon and Colchester, which was slightly disappointing.
"But I cannot grumble too much, because the boys have done really well. We needed to go on that kind of run just to get out of the bottom four."
City host Port Vale at Ashon Gate on Tuesday evening.