Redknapp wrote in his column for The Sun: "Sunderland fans will doubtless be celebrating getting their wish in seeing the back of Steve Bruce.
"Yet unless the men with the purse strings at the Stadium of Light are prepared to loosen them, it won't matter who they get as a replacement.
"Brucie got the bullet when the side failed to reach the expectations on them.
"But I'd ask how realistic those expectations really are right now.
"Because unless you are prepared to pay really big money for top, top players, it is almost mission impossible.
"Steve was basically working in the middle market - and I mean no disrespect to the players there - when it came to transfers.
"Sadly, though, managers find themselves living for today in the current game.
"And that means getting results NOW, rather than seeing that potential gradually realise itself."