Murphy, 23, opted for a move to Leeds for a reported fee of £1million earlier this week after Crewe had accepted offers from the West Yorkshire club, Wolves and Blackburn.
Murphy signed a three-year deal at Elland Road and while assistant manager Neil Baker had been expecting his departure, plans to draft in an immediate replacement have been dashed.
"We had been in negotiations with a midfield player and we thought that was progressing well, but they now appear to have broken down," Baker told the club's official website.
"The player is a southern midfield player, who we pin-pointed as one who would have made a difference to us, especially with Luke moving to Leeds earlier in the week, but it doesn't look as though that is going to progress now.
"We are disappointed that we have been unable to take that forward, but we move on and we have a list of potential targets.
"There are plenty more irons in the fire and we have time on our side, as it is still early July."