The ex-footballer told The Sun that Messenger was a turn-off for viewers because she would not give her colleagues a chance to speak during discussions on the programme.
Messenger announced that she had quit Studio Five in January and made her final appearance on the show on February 26.
Reflecting on his time working with the star, Wright complained: "Melinda would drown us out so many times and it was annoying. People don't want to turn on to see people arguing."
Messenger has so far been replaced by guest presenters who are joining Wright and co-host Kate Walsh. Emma Willis and Natalie Pinkham have been seen filling in over the past few days.
It is thought that the magazine show's producers are currently searching for a new recruit who will become the third anchor on a permanent basis.