The Monaco forward looks increasingly likely to make a loan switch to Everton, who are challenging for a place in the Champions League next season.
The 23-year-old only moved to his French Ligue 1 club at the start of the transfer window but Monaco are prepared to let him go elsewhere temporarily to gain further first-team experience.
Lowly West Ham appeared Traore's likely destination after strong rumours were confirmed when the Ivory Coast international had a work permit hearing ahead of concluding a deal.
Everton's interest has taken West Ham taken by surprise, but Allardyce does not feel the Hammers missed out due to dragging their heels.
"To apportion blame at the end can end up in all shapes and forms," he said.
"All I'm saying is that we could have no more than we did by trying to secure a player of this size, quality and talent. In the end we had a long process of going as far as the work permit.
"It wasn't Monaco and it wasn't us, it was all down to the player's agent. That is who he listened to. That is what happens in today's modern-day game."
Allardyce has only been able to add Wolves defender Roger Johnson to his ranks so far this month as he looks to bring in new recruits to freshen his squad and keep West Ham in the Barclays Premier League.
Everton defender Johnny Heitinga turned down a move to Upton Park after Allardyce thought a deal had been concluded following a meeting, with the Hammers boss aware he is up against the might of other Premier League clubs as he attempts to bolster his team.
Allardyce said: "In this particular time you are fighting with everybody else, you are fighting with lots of football clubs to do deals as quick as you can and as best as you can."
With his struggle to get players into the club, Allardyce would have not welcomed Fulham's declaration of interest in signing England Under-21 midfielder Ravel Morrison from West Ham.
Cottagers boss Rene Meulensteen said last week they had a bid rejected for the player but he knew Morrison wanted to move to Fulham.
Since then West Ham have reported Fulham to the Premier League and Morrison has said he is happy at Upton Park, refuting claims he planned to strike to force through a move.
Allardyce believes the transfer window whips up an annual frenzy and it would be very easy for a young player to get caught up in it.
He said: "This window creates a hysteria about the fact that people will tell you that somebody is going to come and get you. That could then turn your head, probably based on the money that people say you're going to make."
Morrison is likely to start in West Ham's Capital One Cup semi-final second leg against Manchester City on Tuesday night, with Allardyce's side trailing 6-0 after a thrashing at the Etihad Stadium almost two weeks ago.
Allardyce believes Morrison's form has suffered of late, pointing to a groin injury as a reason for him not hitting the heights of earlier in the campaign.
"Recently, from Ravel's point of view, a slight move away from the type of form he did in the early stages was our problem, and his problem," Allardyce said.
"Then we finally found out that perhaps it was down to the groin rather than a dip in the form that he had shown previously. The hard thing for a 20-year-old is to play the level he plays consistently.
"That is the problem with a young talented player: consistency. When he doesn't become consistent then you have to take him out of the team and let him regroup and then come back in again.
"So over the Christmas period we haven't seen a lot of him because of the niggly groins. Now we've seen him as a substitute, and we'll see him a lot more in the near future if he stays fit and plays well."