Reports claimed Barton were closing in on a deal with the Hammers, but that has later been denied by people close to the club.
West Ham fans did not want the club to sign the highly-rated midfielder.
Allardyce told talkSPORT: “I don’t think you need the added pressure if the fans aren’t happy with a player, even as good a player as Joey Barton.
“I had it when El Hadji Diouf trained with us (at Bolton) when I first got there and there was a big reaction against him. You get enough pressure as it is as manager without adding to it yourself.
“So it’s probably the right decision in the end, as much as I am disappointed for Joey.
“We all know he’s got the ability to play in the Premier league, he’s proven that over the years.
“Everyone looks at Joey’s temperament, and I think that’s the only drawback to ‘do you or don’t you’ take Joey on, that’s the only question you ask because it’s not about the football ability, we all know he’s got that.
“If you need a good player with experience in the Premier League and he’s available in a really inexpensive deal, than you’ve got to decide as a manager and as a club whether you want to take that risk on board or not.”