The Magpies suffered a third consecutive loss against their local rivals as they were beaten 3-0 at St James' Park.
Tiote now hopes that the team can restore some pride when they face Chelsea at Stamford Bridge next weekend.
"All I can say to [the fans] is sorry for this defeat again because we cannot accept that," Sky Sports News quotes him as saying.
"It's two seasons now we have been beaten by Sunderland at home and this is the worst, worst thing in my career, so I just want to say sorry to them.
"That's football, we need to focus on the next game now."
Saturday's defeat has seen Newcastle remain in eighth place in the Premier League table.