The Scot, handed what was his first managerial post in the summer, lasted just 13 games in charge of the Blades before being relieved of his duties last Friday.
Weir's sole League One success came on the opening day of the season, leaving United third from bottom in the table with just five points upon his dismissal.
"I've got no complaints because I went in with my eyes open," he told BBC Radio 5 live.
"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.
"I thought we were at the start of something that would be a long-term project and could be successful. I'll only take positive things from my time there."