The move comes after newspaper allegations about a relationship between Bridge's former partner Vanessa Perroncel and Terry, who was stripped of the England captaincy by Capello in the wake of the headlines.
"I think it is a blow for England and Wayne Bridge," said Blackburn boss Allardyce on Friday. "World Cups don't come around very often and with the good form England are in they could be doing better in this World Cup than they have done for many years.
"But he has had a long hard deliberation over what he should or shouldn't do and he feels he shouldn't be there. We have to respect that.
"There is more to life than football and he obviously feels the right thing for him is not to take part. It is a great shame for him."
The decision is a blow to Capello, who has injury concerns over first-choice left-back Ashley Cole and would surely have deployed Bridge in his place.
And the Rovers boss believes former Blackburn man Warnock is the right man to fill Bridge's boots.
"After that you have to look round the country and you have to point to our old left-back Stephen Warnock," he said.
"He's playing for a team that could finish in the top four, are in a major cup final on Sunday and could be in the FA Cup final as well.
"He has had a fantastic season and form suggests he would be the right replacement to fit in if Ashley Cole is not going to make it through injury."