"At least three in the first half", he told BBC Sport.
"I think it is highly unlikely we will see him again this season". He faced the Sky cameras after the game, in which he admitted that it "wasn't good enough" that Everton "crumbled" having led 1-0.
The Republic of Ireland worldwide would have been doubtful for the Everton game with the Clarets after he suffered a set back when he was injured during their 3-1 win over Crystal Palace earlier in February, but he is also expected to be available.
The visitor's worries were further worsened with Williams getting sent off for a foul on Barnes during an Everton set-piece.
Phil Jagielka took the armband when Williams was dismissed, Everton fans feel it should have went to Coleman while plenty also believe the Ireland captain deserves the same role with his club on a permanent basis. I go home and say to myself 'How do I put this right?' For me to see the players under-perform in the second half is very disappointing for me.
Asked about the crowd's response to Tosun's withdrawal, Allardyce said: "It happens".
Everton, with just one away win this season, had gone ahead in the 20th minute with Turkish striker Tosun's first goal for the club since he joined from Besiktas in January, a fine header after Seamus Coleman had flicked on a Theo Walcott cross. "It's my problem to sort it out", he said.
Everton started the game as a more dominating side with heavy pressing and continuous pressure on the Burnley backline.
"At the moment we're in a very good position and I'm slightly surprised by the speculation".
The Burnley right-back put in a solid defensive performance and provided a fantastic through-ball for Barnes' victor.
Ashley Barnes scored for the second Premier League game in a row to level after the interval, beating the otherwise impressive Jordan Pickford at his near post. But that will and demand, the players here have underling honesty to what they want to achieve. We wanted to correct the run and we have done that.
"I think the second half was more about Burnley playing with Wood up front and Barnes and us not coping with the more direct style of play they chose to use".