The 24-year-old Trinidad and Tobago international helped to lift the Black Cats out of the Premier League's bottom three, albeit briefly, last weekend with a double in the 4-0 rout of West Brom.
However, Jones and his team-mates head for surprise package Hull on Saturday knowing they need to build upon that foundation if they are to drag themselves clear of the developing scrap at the foot of the table.
While West Brom and Blackburn, who have appointed Sam Allardyce as manager, are in danger of being cut adrift, just five points separate Sunderland in 18th place from Portsmouth in eighth, and Jones knows just how important a consistent run of results could be.
He said: "The thing is, from eighth place to last place in the league, it is so tight, so I don't think any teams in those positions will be thinking it is going to be a relegation battle.
"It's just like the Championship, or League One or League Two, where I have been for years, you have a couple of wins and you are right up the table; you have a couple of losses, and you are back down.
"That's what's happening this year. All we need to do is just maintain that progression.
"One win gets you so far. We are not really going to worry about relegation until it has separated, and at the moment, it has not.
"There are a lot of big teams down there and you don't know what is going to happen.
"Every game from now until the table irons itself out and there is some space in between the relegation zone and mid-table, we need to be on that type of form and winning games until that time comes.
"Whenever that is, we don't know, but hopefully it will be in the next three, four, five games.
"We just need to keep progressing."
Keane's resignation came after a 4-1 home drubbing by Bolton - their fourth on the trot at the Stadium of Light - extended their depressing run to six defeats in seven games.
Caretaker boss Ricky Sbragia came close to addressing that situation in the most unlikely of surroundings when he took his side to Manchester United in his first game and left with only Nemanja Vidic's late strike denying them a famous point.
He did enough in his first week at the helm to persuade chairman Niall Quinn that he had to be considered as he searched for Keane's successor, and events since have simply enhanced his reputation within both the boardroom and the dressing room.
Whether that could eventually lead to his permanent appointment remains to be seen - Ladbrokes are quoting him as a 9/4 favourite - but there is growing support among the players for his candidacy.
Jones said: "We have been working with Ricky. He has our respect and we have his.
"He is basically continuing the work he has been doing behind the scenes and just trying to take the club and the team forward.
"The only thing you could do was be happy for him is he was made permanent manager.
"At the same time, he is just doing his job. But you don't have control.
"A new manager could come in and get rid of all of them, so you don't have control of the situation.
"All we have to do right now is just work together and work for the team, work for the club and see how far that gets us."