The ex-Newcastle United boss immediately pointed out fitness problems.
The veteran Premier League manager replaced Dick Advocaat at the Stadium of Light early on in the 2015-16 season, with the Black Cats failing to win any of their first eight league matches at the time.
The North-East side remain in something of a precarious situation, as Allardyce's men sit 18th in the table, one point behind 17th-placed Norwich City - albeit with a game in hand.
Defoe is convinced that their woes stem from that dreadful start under Advocaat, and staes that the first thing Allardyce said upon taking the job was that the players were not fit enough.
"It's happened because of the start of the season. We just weren't good enough and we weren't fit enough," he said to the Journal, via Sporting Life.
"If you look at the fitness stats now - the running stats and the high intensity stats, that side of it - we were so far off, so far off where we are now. Look at the [opening day] game against Leicester - we were blown away. It was difficult.
"Now it's like a different team. The first thing the manager [Allardyce] said when he came in, we had a meeting and he said, 'You're not fit enough. I'll get you fit and that's all you need' because we've got top players and internationals."
It gets no easier for the Black Cats, who host Arsenal at the Stadium of Light tomorrow. However, with the Gunners looking somewhat out of sorts, supporters might be optimistic that they can turn over the North Londoners.
Their survival won't hinge on victory, given their game in hand, but it would go a long way to help keeping them in the top flight.