Advocaat arrived at the Stadium of Light in March, following Gus Poyet's departure, and oversaw a 1-0 defeat at West Ham prior to the international break in his first game in charge.
Both Poyet and predecessor Paolo Di Canio secured derby victories in the second game of their respective tenures, but Elliott feels Sunderland's problems could prove too much for the Dutchman.
The former full-back, who spent 11 years at St James' Park as well as a brief spell at Sunderland, told Perform: "I'm not sure the change in manager at Sunderland is going to be enough for them.
"There are deeper problems than what the manager can overcome, it's going to be a huge game and I think we've got a better chance of beating them at their place than we've had in a long while.
"For weeks before, you can just feel the tension building. It's more than a game and I'm sure the new players are aware of that.
"History will tell [Advocaat's arrival] will help them but I've a feeling - I think the second half [of Newcastle's defeat] against Arsenal was probably the best we've played for a long time.
"It's a shame there's been an international break because taking that into the derby would have been fantastic."
