Hermann Hreidarsson's 24th-minute strike, his first goal since 2009, secured Pompey a sixth straight win which keeps their slim play-off hopes alive.
The beleaguered Blades, however, remain in the Championship relegation zone six points from safety.
Cotterill said: "It was just the ticket - another win. It was pleasing. It was a difficult game. Sheffield United are down there and they are obviously fighting for their lives. So we knew it was going to be tough.
"What we didn't want to happen was to get to the last 10 minutes of the game with the score only 1-0. We knew there would be a lot of big balls into our box throughout the game. We had four up against our four defenders. There is no room for error with any of that.
"Had we taken our chances in the first 10 minutes, we could have been 3-0 up. That would have put a different slant on the game completely."