Weir, who launched his first game as a manager with a win as the Blades clinched a 2-1 success over Notts County on Friday night, is anxious not to put his new charges under any unnecessary pressure after the club's successive play-off failures in Sky Bet League One.
Asked if the squad talks about promotion, the 43-year-old Scot said: "No, we don't. That's a long way away. I think we need to focus on the process rather than the result.
"That's the biggest thing for us. We need to focus on what we need to do in order to be successful, rather than just thinking about success and what it brings.
"When we first came in we spoke a little bit about the disappointment of the last two seasons. We addressed it and we can't pretend it didn't happen, but it's a new regime, a fresh start and the players have to shake that off.
"There's nothing surer in football than you're going to have disappointments, but it's how you respond to them."
The Blades take on Burton in the first round of the Capital One Cup at Bramall Lane on Tuesday night.