Allardyce took charge at Sunderland back in October, with the North East side sitting rock bottom of the Premier League table.
However, Defoe says that the 61-year-old was keen to ensure that the Black Cats’ squad did not panic - regardless of the situation they were in.
"The manager has always been calm," Defoe said. "He came in the first day and said I will give you the basis how to win games and then you have to go out there and do it."
"It is as simple as that. Training is always good with a game-plan and the squad is confident at the minute. I suppose being in a position like this you know you have to raise your game, you give a bit more.
Despite Allardyce’s words, there have still been times under his stewardship when Sunderland could have collapsed.
The Black Cats recently lost five fixtures in a row, and fell seven points adrift of safety.
However, after wins against fellow strugglers Aston Villa and Swansea City, optimism is flooding back to the Stadium of Light again.
Sunderland are still in the relegation zone, but they are now just one point behind Swansea and have moved ahead of Newcastle United.
Sunderland’s next match comes this weekend against Tottenham Hotspur, and if they are victorious they could move out of the drop zone and take a big step towards survival.