The Blades have lost four and drawn one of their five League One games following an opening-day success over Notts County, with their second-half performance in last Saturday's derby defeat to Rotherham a particular low point.
That showing was in stark contrast to their first-half display at New York, which showed promise.
And Weir knows his men are not far away from hitting their straps.
"You have to try and take the positives, that's my nature," he said. "I was very disappointed after Saturday's game and I can't hide that, but there'd be something wrong if I wasn't.
"That's the most frustrating part, I genuinely feel we are close to where we want to be and have made a lot of progress.
"We are so near yet so far and I know that might sound like I am making excuses but that is genuinely how I feel.
"There are a lot of positive things going on but ultimately you are judged on results and that will always be the case."
The Blades head to Carlisle on Saturday aiming to put things right, but they come up against a side reeling from the sacking of boss Greg Abbott earlier this week.
Weir admits that could make things tougher for his men, but he has prepared accordingly.
"It will have been hard anyway to be honest because all games at this level are a challenge," he added.
"We see teams have a reaction when they change their manager and time will tell whether that is the case.
"But we have planned for that, we have planned for them to be up for it.
"But it throws us slightly to what they will do because they will have a new man in charge and he may have new ideas so it makes it a little more complicated.
"We want a reaction of our own, it was a disappointment for us at Rotherham having got into a position to get something out of the game, so it's important we will be having a response.
"You have got to show resilience and believe in what you can do."