The former Rangers and Scotland defender was removed from his first-ever managerial post last Friday after 13 matches in charge of the League One outfit which heralded just two wins - one of which came via a penalty shoot-out in the Johnstone's Paint Trophy against Scunthorpe.
With only one league triumph during his four-month tenure, Weir, 43, leaves the Blades toiling at the foot of League One, having started the season with promotion aspirations.
And, despite expressing his disappointment at the lack of time afforded to him, he understands the reasons behind his dismissal.
Weir conceded: "I've got no complaints because I went in with my eyes open. 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."
After seeing his maiden managerial role end in failure, he is in no rush to make a quick return to the dugout.
Weir added: "I think it's important for Lee (Carsley, assistant manager) and I to speak about what went on.
"We need to look at the positives and the negatives and what we've learned. To jump straight back in would be difficult.
"We'll definitely be better coaches for it and we'll look to put what we learned into practice."