The Scot had been in charge of the Blades for 10 matches before he was dismissed last week.
During his brief spell at the helm, Weir guided the League One side to just one win.
"I've got no complaints because I went in with my eyes open," he told BBC Sport.
"I felt like the players were on board with what we wanted, but we just didn't get the breaks.
"I don't think 10 league games is long enough to get your ideas up and running, but I understand because results were poor and people start to get worried."
Former Derby County boss Nigel Clough is the favourite to succeed Weir at Bramall Lane.