The Premier League champions secured the signature of midfielder Marouane Fellaini from Everton on deadline day, representing in the club's only major signing of the window.
Former Liverpool and Tottenham Hotspur director Comolli believes that United are in need of a new figure following their failed attempts to sign the likes of Cesc Fabregas from Barcelona and Athletic Bilbao midfielder Ander Herrera.
"If there was a club in need of a director of football to ease the process for both individuals it was Manchester United," Comolli told BBC Radio Five Live.
"David [Moyes] only joined on July 1, which was quite late. The issue for Manchester United is that the two most important people at the club, in Sir Alex and David Gill, left their positions and new people came in for their first transfer window."
New United chief executive Ed Woodward has been criticised for his conduct during the summer window.