Allardyce has questioned the wisdom of the Premier League letting Saturday's match at Stamford Bridge proceed, after Blackburn informed them of the first two cases of swine flu in their squad.
And he believes it is possible the virus could have been spread to the Chelsea camp.
"There is no doubt about that," Allardyce said. "When you look at the medical side of it, it is one of the most infectious viruses we have had."
Allardyce is adamant Blackburn have operated by the book, by informing league authorities and letting them determine the next step of action.
He said: "They know that we went through the right procedures and that we did not call it off because we couldn't.
"There was no point in trying because back in February or March they told us we had to get a team out there, no matter what.
"It is their responsibility to consider how dangerous it might be to allow this to spread throughout football so they have shirked responsibility - not us. I don't think they have put much thought into it at all."
A similar case in France at the weekend saw Paris St Germain's match at Marseille postponed.
PSG's Ludovic Giuly and Mamadou Sakho were diagnosed with the virus on Saturday and the confirmation of a third case in the squad on Sunday prompted Ligue 1 authorities to act.
Two members of PSG's coaching team had also reported symptoms of swine flu.
Last night the Premier League responded to Allardyce's concerns, by stating: "As ever, when it comes to health matters the Premier League will be guided by the relevant statutory authorities.
"If a club postpone any of their matches they would have to prove they were unable to fulfil their fixture, however we do not anticipate, at this stage, any circumstances under which a match could be justifiably postponed."
Meanwhile ahead of Tuesday night's game Allardyce claims Peterborough manager Darren Ferguson has inherited the managerial magic from his father Sir Alex.
Ferguson guided Peterborough to successive promotions in the last two seasons.
Posh finished second in League Two in Ferguson's first year as a full-time manager, before repeating the feat in League One last season to earn promotion to the Championship.
For the time being it seems the Midas touch is something that runs in the Ferguson family, and Allardyce for one is convinced that a great deal of wisdom has been passed on from father to son.
Allardyce said: "For a young man dropping into his first job, it can often be a tough time in terms of making a team with fewer finances, and sometimes your inexperience can cause you a problem.
"But it hasn't for him and he has obviously inherited a lot of the top qualities of his dad."
Barclays Premiership. Click here to bet.