Yohan Cabaye had given Newcastle a 1-0 lead before a late own goal from Demba Ba gifted Sunderland a point, and Simpson believes that Sunderland were "lucky" to prevent his side from claiming the three points.
Simpson said: "I thought we were going to do it.
"It gets to the point in a game when you do not think you are going to concede. You feel quite comfortable. Everybody seems to be doing their jobs and playing together.
"For them, it had to be something freaky like that. It was a fluky, lucky goal."
The 25-year-old has featured six times for Newcastle this season.