The current Barclays Premier League table suggests those three clubs will be battling over the remaining weeks of the season to avoid being the team which joins Burnley and QPR - who are in even greater danger - in next season's Sky Bet Championship.
The Black Cats are currently in the bottom three, but just a point behind Hull and Leicester - who visit the Stadium of Light next weekend - and two shy of the Magpies.
But Advocaat, whose side have a game in hand on the others - albeit away at Arsenal ahead of a final day trip to Chelsea - has challenged his players to keep their fate in their own hands as they head for Everton on Saturday.
The 67-year-old said: "I don't care at all
I only care about our club
I don't care about Newcastle or Hull or whatever.
"We have to do it by ourselves and not look too much to other teams
We have to do it on the pitch and show them what we want.
"That's the most important thing - but everybody is counting only the first two games
They are important, but we still have two games to play against Arsenal and Chelsea as well.
"Everybody is counting those already as nothing, and I don't see why."
There were anxious eyes cast towards television screens on Wearside, Tyneside and in the east midlands on Monday night as Hull hosted Arsenal and lost 3-1, but it proved of only passing interest to Advocaat.
He said: "I take an interest, of course, but we have to do it by ourselves
I'd be lying if I said I was not happy with the result on Monday so in that way, it was good for us.
"But we also still have some very important games at the end, so let's wait and see
Tomorrow's is the most important game now against Everton."
Sunderland ended a run of six successive league defeats at Goodison Park last season when Ki Sung-yeung's first-half penalty was enough to see off the 10-man Toffees, and tangible reward for their efforts this time around could prove crucial with the Dutchman having been forced to recalculate his points target despite collecting seven from his first five games at the helm.
He said: "When I started, I said six, seven points must be enough
But I think we need three, four more
But that's possible."
Advocaat will be without skipper John O'Shea on Merseyside as the former Manchester United man, who had not missed a single minute of the campaign until injury intervened during the win over the Saints, sits out with a rib problem, while £10million signing Jack Rodwell has succumbed to a hamstring strain.
But striker Steven Fletcher is back in contention following his ankle injury, and defender Wes Brown makes a timely return to the squad for the first time since damaging a knee back in March.
O'Shea, who will travel with the squad as he attempts to recover in time for next weekend, will be a miss, but Advocaat is confident the gap he leaves can be plugged.
He said: "We can't take any risks with John O'Shea because we still have important games to come
He was not 100 per cent fit, so we can't take any risk with that.
"The good thing is that Wes played on Monday a half-game with the second team and trained this week, so he looks good."
Source : PA
Source: PA