The former Everton, Rangers and Scotland defender had his contract at Bramall Lane terminated in October after only 13 games at the helm.
The 43-year-old left the Blades 22nd in the League One table having failed to win since the opening fixture of the season and on the back of a Johnstone's Paint Trophy defeat by League Two strugglers Hartlepool.
"I don't think 10 league games is enough for anybody to try to implement what they are trying to do," said Weir, speaking at a Tesco Bank Football Challenge event at Toryglen Regional Football Centre in Glasgow.
"So regards to getting a fair crack of the whip, I don't think I did.
"That's not a long enough period of time to try to do what you want to do.
"But that's the industry and that's the way it works. Unfortunately you don't get enough time.
"I was ready (for the job). Circumstances changed there and it was difficult, as all jobs are and it never worked out the way I would have liked but it was a great experience.
"I learned a lot and I will be better for it. You move on, you don't look back and try to change the past.
"I didn't want a break but you try to make the most of it, to spend a wee bit of time with your family.
"You don't really get that option when you are in the job so it has been good. I have enjoyed it but I don't want it to last too long.
"I definitely want to get back involved full-time, it is what I do, what I have done for a long time and I really enjoy it."
Weir claims the set-back in his first managerial post only makes him more determined to succeed.
The former Falkirk and Hearts player will consider jobs north and south of the border although he was reluctant to talk specifically about Inverness, who look to be losing their manager Terry Butcher to Hibernian.
"I think you always have something to prove to yourself," he said.
"You can't rest on your laurels and sometimes when you have a setback then it makes you more determined to be a success the next time.
"The industry changes very quickly. People are in a job and out very quickly, that's not going to change.
"There are plenty people for whom it hasn't been a success straight away and eventually it has and you draw comfort from that.
"I have spent a lot of my career in Scotland and had a lot of good experiences in Scotland as well as in England.
"I wouldn't rule out anything out. I am open to any opportunities, I don't limit myself.
"But I don't want to start talking about individual clubs and situations at specific clubs.
"But like I say, I want to get back coaching, I want to get involved."
- Sports & Recreation