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 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 (done) 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 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."
A deal for Inter Milan forward Ishak Belfodil never got off the ground but, with club-record signing Andy Carroll making his way back to first-team fitness and a new contract in place for Carlton Cole, Allardyce at least has more attacking options than earlier in the season when the Hammers' profligacy in front of goal was a major factor in them slipping down the table.