Without a win since the opening day, United sacked David Weir on Friday and lost 3-2 to Coventry on Sunday after falling three goals behind early in the second half.
They did battle back to score twice and set up a tense finale but could no't complete the comeback.
Morgan said everything is in place for the new man, however.
"He's got a fantastic foundation of a football club to work with," he said.
"The supporters, the stadium, the academy, the infrastructure and the squad of players, it's a good job to be inheriting.
"It's a good job to be coming into, at a good time of year. But it's all very well changing the manager, we've had two in the past six months, but we can't keep changing managers.
"It comes to a time when players stand up, players are counted. Players play the game. As coaches and managers you can do what you want from Monday to Friday, you can set them up, you can drill them as much as you want, but the players play the game.
"I'm not sure about the timescale but I am sure the club want to get somebody in as soon as possible because we have another big game coming up next week against Port Vale."
Leon Clarke put Coventry in front after six minutes, before Callum Wilson smashed in his 10th of the season moments before the break to make it two.
Clarke added the third after 49 minutes but when substitute Lyle Taylor fired his 62nd-minute free-kick through the wall and into the net, the momentum shifted.
Taylor headed a second 10 minutes from time but City clung on.