Mancini reportedly held talks with eight clubs in the summer.
Asked if he had proven the Italian's equal tactically, Allardyce - who on Friday admitted he had given up on managing one of the top four - said: "Wow! That's a question and a half, isn't it, that one?
"No clubs talked to me in the summer, so what does that mean?
"I'm just glad that I'm back where I've been for a long, long time and I like pitting my wits against every manager in this league.
"It's been a fantastic thrill for me over the last 12 years or so, at Bolton, Blackburn and Newcastle, and here now, to go out in the best league in the world and most entertaining league in the world."
Yet, he could not resist adding that the Hammers' "tactical plan" had "mastered the champions of the Barclays Premier League".