"You have got to be strong at this level," Warnock said. "I thought we were a little bit weak mentally last year and I don't think we would have won this game last year. I do feel we're better equipped.
"I think we can get a lot better," he added. "We didn't play great on Saturday but we won 4-1 and we didn't play great here but we were solid. We've still got a bit of work to do but it's pleasing."
Warnock is also targeting a replacement for Sunderland-bound Andy Gray and said: "Poor Shippy [Neil Shipperley]had to do 90 minutes. He was knackered after an hour but he had to stop on, bless him.
"We'll be looking for another striker over the next couple of weeks and take some pressure off him."
The Blades were in front inside five minutes against Burnley when Danny Webber crossed for Shipperley to score his first goal for the club at the near post. Chris Morgan added to that advantage five minutes before half-time in scrappy circumstances. The defender met Michael Tonge's corner and his header was punched away by the Burnley goalkeeper Brian Jensen but deflected back into the goal off Morgan.
Burnley never gave up, Ade Akinbiyi pulling a goal back in the 72nd minute and their manager, Steve Cotterill, felt his team were worth at least a draw but, having lost 2-1 at Crewe on Saturday, they remain without a point this season.
Cotterill said: "I thought we were very unlucky to be going in 2-0 down at half-time and we definitely did enough to get something out of the game.
"I thought we should have got something from that performance and on another day that will be more than good enough for a win.
"We had some good chances and played some good football and we haven't got any gripes whatsoever. We could have done better with the goals but other than that we were a million times better than we were on Saturday. As long as we carry on with those performances, we will get the points."
Elsewhere in the Championship, Queen's Park Rangers have also started the season well. The QPR manager, Ian Holloway, spoke of his desire to model his management style on Jose Mourinho after guiding his team to a 2-1 win over Ipswich Town which gives his side four points from two games.
First-half goals from Kevin Gallen and Martin Rowlands were enough to give Rangers victory, although they experienced some nervous moments after Sam Parkin scored his first goal for Ipswich early in the second half.
But although he was delighted with his side's display, Holloway will continue to demand more from them throughout the season.
"That was one of the best performances from any team I have managed - but I still wasn't happy with them at half-time," Holloway said. "I told them they should have been in front by more than two goals. That prickly character at Chelsea [Mourinho] could teach us a lot about those things. If two flies were crawling up a wall, he would want one of them to win - and I want to be more like that."