After a long, hard battle for survival, Allardyce's side secured their own safety and sent their arch-rivals down in one blow with a 3-0 win over Everton on Wednesday night.
Such is the intensity of the rivalry between the two clubs that in the days since that match, most Sunderland fans have taken particular delight in having been the direct cause of the Magpies' relegation being confirmed.
However, Allardyce, who managed Newcastle in a brief stint in 2007-08, believes that his former side's relegation is something to be mourned even by the supporters of his current team.
The 61-year-old told Sky Sports: "I personally think it's good for the area to have both clubs fighting against each other, it's a terrific derby, a terrific occasion.
"This one is special like them all. To lose it, I think, is a blow for the area."
Both North East clubs have been in the Premier League for each of the last six seasons since the Magpies' single year in the Championship following their last relegation in 2009.
Having two derby matches every campaign, as well as the general struggle for ascendancy in the area, has given the recent years more of an edge for both clubs, something which has particularly intensified with the rivals both battling relegation.
However, next season Sunderland will have to settle for a rivalry with Teeside club Middlesbrough after their promotion from the Championship.