Barnsley-born Morgan, 35, who spent nine years as a player at Bramall Lane, has been placed in charge until the end of the season following the surprise sacking of Danny Wilson with just five games remaining.
Wilson's 23-month spell in charge ended in the sack on Wednesday and club owner Kevin McCabe revealed in a press conference on Thursday it was the Blades' stuttering home form that had cost the 53-year-old his job.
United have won only seven home league games this season, drawing nine and losing four, but the club can still gain automatic promotion.
Despite sitting sixth in the table, they trail second-placed Bournemouth by six points with two games in hand.
When asked why the Blades had struggled in front of their own fans, Morgan, who said he had been shocked by Wilson's departure, added: "I've no idea. If I knew the answer I'd have aired it before now.
"Is it pressures from playing at home? Is it the big crowds? Do we freeze?
"The team structure is there, the players are there, the ability's there, so there has to be something and we'll have a look at it and address everything we can.
"As coaching staff we can only do so much and like I said to the players this morning, they've put themselves in a fantastic position and it will be them that clinch it, or let it go."
Wilson's side were on the verge of automatic promotion last season but faltered after leading goalscorer Ched Evans was jailed for rape and lost out in a penalty shootout to Huddersfield in the play-off final.
The club brought in Nick Blackman from Blackburn in the summer but have struggled for goals since his departure to Reading for £1.2million in January.
Morgan, forced to retire as a Blades player due to a knee injury sustained in 2010, became reserve team coach at Bramall Lane soon after.
He said: "Danny's always been great with me and has always said I had all the characteristics to have a career in coaching, as an assistant manager and as a manager, he's always been very open.
"I spoke with him yesterday and he said if the opportunity is there, take it and enjoy it.
"That is the measure of the man because he's just been relieved of his duties and he's got enough about him to wish somebody else good luck.
"That's how he is. I owe a lot to him, both for my playing career and obviously getting me going in my coaching career as well.
"He gave me my debut as a player (at Barnsley) and got me involved in this side so I'll always owe him a lot."
McCabe, who stepped down as club chairman at the end of 2010 but who remains the club's owner, said a change in manager would hopefully bring the best out of the players, especially at Bramall Lane.
"I believe Chris has got a way of leading Sheffield United to get more out of the team at the moment and hopefully get us across the line," he said.
"For some reason we're unsuccessful at Bramall Lane and that's a statistical fact.
"It's perplexing but it's a fact and I'm hoping that Chris and his style will make us successful at Bramall Lane in the remaining three (home) fixtures.
"Our exemplary away results speak for themselves, so that's my feelings and they're shared by people on the club board.
"Passion is an over-used word but Chris has got leadership style that includes aggression, and that's said in a proper fashion, that may get more out of the players."
McCabe ruled out a possible return to Bramall Lane for former manager Neil Warnock.
When asked directly, McCabe said: "No, probably not."
Warnock was sacked by Leeds following their recent defeat at home to Derby.