Allardyce took the reins at the Stadium of Light early last month, replacing Dick Advocaat, and has since guided the Black Cats to their first win of the Premier League season.
Despite losing three of the four fixtures under Allardyce, defender Jones feels that the Wearside outfit are on the way up such is the influence of the former West Ham United boss.
"I've been really impressed with the gaffer and the work we've been doing on the training pitch, but it's not just that and we do a lot of work after the games watching videos and seeing what we need to improve on, so if there is a performance that hasn't been good it's not just swept under the carpet," Jones told the club's official website ahead of Monday night's trip to Crystal Palace.
"We analyse it straight away and look at personal and collective improvement, and in the position we are in at the moment we need to be improving as a team and as individuals to move up the league.
"Last season the [Palace] game was highlighted as one we needed to get a win from to kick on because we were in a little bit of a rut, but it was a massive win and hopefully we can emulate that on Monday."