Boothroyd, who was on the pitch clapping the City support on the final whistle, told the Press Association: "I'm delighted with that result. Sheffield United are probably the best team we've played this season and we've come away with the result.
"To be honest, they will feel a little bit hard done by. They've hit the woodwork twice and went close on a few other occasions, but we did what we had to do.
"We stood firm when we had to and played football when we could. That was a good combination. The scoreline tells you that. Andy Reid came on for them and he's a Premier League player.
"He's got top-flight quality and he'll get even better when he gets fit. The more games he plays for them the more dangerous he's going to be.
"We swapped things around a little bit as the match wore on because we knew we were going to come under the cosh, and we did.
"But the lads showed a lot of heart and guile to weather it when we did. That gives me a lot of satisfaction and I'm pleased with the way we are progressing.
"I don't care what anyone says, this is always a very tough place to come."