Allardyce took over Dick Advocaat at the Stadium of Light last month, and he is still trying to put his stamp on the squad.
Although the Black Cats have improved slightly – they have won just one of Allardyce’s first four matches in charge.
However, Jones still believes that the 60-year-old boss is doing a good job, and he has been delighted at how thorough Allardyce has been.
“He’s been really good. I’ve been really impressed with the gaffer, to be honest," he said.
“I’ve been impressed by the work we have been doing on the training pitch, and not just that, but all the work we do after the game – watching videos and working out what we need to improve on and what we did well.
“It’s very much, if there’s been that performance that hasn’t been good, it’s not just been swept under the carpet.
“Straight away we are looking at it and working out what we can do better as individuals and as a team. In the position we in at the moment, that’s what we have to be doing.”
Allardyce guided Sunderland to their first win of the season over Newcastle United, but they have failed to build on that performance.
Although there has been some signs of encouragement, defeats against Everton and Southampton in their last two matches have put them in serious trouble.
Sunderland are currently four points away from safety, and they return to action with a game against Crystal Palace on Monday evening.