The Dutchman left the Stadium of Light all the way back in October, with Allardyce swiftly been named as his replacement at the club.
His exit came amidst a disastrous start to the season, in which he claimed that the side did not possess enough quality to avoid relegation from the Premier League.
They did avoid the drop though; with a comprehensive win over Everton on Wednesday securing their top-flight status at the expense of rivals Newcastle United.
And Allardyce has admitted it was sweet to prove his predecessor was wrong about the squad.
“Sweet is proving Dick wrong,” he told the Sunderland Echo.
“It was a challenge when he said that this team is not what I want to be associated with and that they will get relegated.”
“We have gone and proved him wrong, which is great. I have come and done the job, it is more satisfying for the players.”
Sunderland will now be hoping that they can establish themselves under Allardyce and avoid survival scrambles in future.
The Black Cats have flirted with relegation for a number of years, as a series of managers have come in and saved them from the drop following disastrous starts.
That has hopefully come to an end under Allardyce, who will be keen to enjoy the kind of success he had at Bolton and West Ham at the Stadium of Light.