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9th November 2017
06:17pm GMT
And while most of Sullivan's tweeting is harmless, Allardyce has warned that there are occasions whereby it can actually be detrimental to the Hammers.
"I couldn’t control David Sullivan," Allardyce said on talkSPORT. "He is the owner of the football club and however negative you told him those comments might be from Jack, he was always going to give Jack that information and let him tweet it.
"You pull your hair out at the beginning and in the end you have to accept it for what it is and move on and accept that it is going to happen.
"Some of the time those tweets were really unacceptable, particularly the one about Kevin Nolan, who was an outstanding captain for West Ham.
"When it gets too personal towards one player particularly, it needs to be reined in. But you can’t stop it."
That particular tweet referenced by Allardyce was one sent by Sullivan in 2015, when he suggested that Kevin Nolan should be playing in League 2 rather than for West Ham.
The leaking of information from a club can understandably be a cause for concern among managers and while Allardyce didn't suggest that Sullivan was to blame for the fact that a story about the recently sacked Bilic phoning West Ham players asking where he went wrong made it to the press, he rightly condemned the anonymous source.
"I don’t know who leaked that in the press. Whoever did is disgusting," Allardyce said.
"Slaven ringing up one or two of the players for a private conversation and it ends up in the press.
"If he has been too soft, then they have opened themselves up for a more disciplined regime [under David Moyes] and they can’t complain about it."Explore more on these topics:
