The Magpies took on relegation rivals Norwich City at Carrow Road on Saturday in desperate need of all three points to avoid the drop.
Instead the points went to the Canaries, as a 93rd minute goal from Martin Olsson saw them secure a 3-2 win in dramatic fashion.
The result leaves the Magpies 19th in the table and six points from safety with seven games remaining, and Savage believes they are now doomed for the drop.
"What a result for Norwich. Newcastle, defensively, were so poor,” he told BBC Sport.
“They are now six points behind Norwich - they have a game in hand but that is against Manchester City. Aston Villa are doomed, and so I think are Newcastle."
The situation certainly does look dire for Newcastle United at this stage of the season.
The one positive is that they currently have a game in hand over the Canaries but given that is against Manchester City, who returned to their best in a win over Bournemouth on Saturday, three points will be hard to come by.
Given their remaining fixtures also include Liverpool, Southampton and Tottenham and it is hard to see where they will get the points they need to stay up.