Paul Hart won his first game as Palace manager
Hart took over from Neil Warnock last week and only had three days to work with his new team before Saturday's win over the Blades.
The Eagles manager said that he had been hugely impressed with the players during the short time that he had seen them, but predicted many more twists and turns before the season ends.
"I thought the performance was excellent," he said. "When you play against Sheffield Utd, they are a very tough team, you always know that you've been in a game when you play them.
"So you have to start with the basics, head the ball well and that's what we did. In spells we played some decent stuff but all over the pitch we did what was necessary.
"Their set pieces were a threat, but we defended pretty well and on another day we could have tucked away another two or three chances as well.
"We haven't attempted to come in and make massive sweeping changes I think that would be fool hardy, we've just come and tried to help. That's what we're here for, the deal is until May 2 and we hope to keep this club in the division.
"There will be ups and downs because it's hard when you are down there. The players haven't done much wrong themselves, but when you are down there tricks are played and there will be ups and downs along the way."
The defeat was Sheffield United's sixth consecutive loss on the road, but Blades boss Kevin Blackwell argued it is always hard playing against a side who have recently changed manager.
"Palace fought like dogs," he said. "They battled all over the pitch and we just didn't create enough chances.
"I think Palace will be fine. Neil [Warnock] is the biggest bluffer in the league, he was always moaning about the lack of strength in the squad but these are a good strong bunch that he had here."
Palace will be hoping to build on the victory over Sheffield United when they take on Bristol City at Selhurst Park tomorrow night.