Allardyce said he was "shocked and disappointed" after being axed on Monday despite the club winning four of its last seven league games and being five points off the top six.
GEAR:Save up to £10 on Blackburn shirts with Kitbag. Free delivery on orders over £40
The decision was labelled "absolutely ridiculous" by Manchester United manager Sir Alex Ferguson but processed chicken giant Venky's, who bought the Lancashire club for 23 million pounds last month, have moved to justify Allardyce's dismissal after two years in the job.
"We do not mean anything bad for Sam Allardyce but we feel that we need to take the club up in the league and grow," Venky's chairman Anuradha Desai said in Tuesday's Lancashire Telegraph newspaper.
"We want Blackburn Rovers to be fourth or fifth in the league or even better. It is nothing against Sam but we have a different vision looking forward and we want the club to grow.
"We had been talking to Sam in the past few weeks but he did not fit in with our vision for the club's future.
"We wanted good football, wanted the games to be interesting and of course wanted to win and to have good players."
Desai said they would ideally find a British replacement, although they were in no hurry.
"The fans should trust us and have belief in us because this is in the best interests of the club," she said.
"Our thinking now is that it will be a British manager, but we are open if there is an outstanding candidate: someone who would be really, really good for the club."
Assistant coach Steve Kean will take over first-team duties until Rovers find a new manager.
"It could now be a couple of months before a new manager is put in place," Desai said.
NEWS:Blackburn sack Sam Allardyce
NEWS:Allardyce shocked and disappointed by sacking
How to watch Manchester City vs Arsenal: Live streams for WSL match
‘Arsenal’s Class of ’83 would give Man United’s Class of ’92 more than a good game – It’s a scandal that youth team isn’t talked about enough, if at all’: Martin Keown believes the Gunners team he grew up with doesn't get anywhere near enough credit
