Allardyce was sacked by Rovers in December 2010 by new owners Venky's, who went on to suffer the pain of relegation under Steve Kean.
The Hammers boss saw two of his former clubs relegated as Bolton Wanderers followed Rovers into the Championship.
Alardyce told The People: "I have to say there wasn't much feeling when Blackburn were relegated because of the way they treated me.
"Bolton is a different story because I left them and I only did that because of their lack of ambition.
"Everyone knows how much the club means to me and always will, so I was saddened by their relegation."
Allardyce swapped places with his two former clubs after winning promotion with West Ham United via the playoffs last season.