The club decided over the weekend that Parkinson was not the right man to lead the club forward and showed him the Stadium of Light exit door.
Sunderland have turned to Taylor to take charge on an interim basis and he will lead the team into their League One clash with Burton Albion on Tuesday night.
The 34-year-old, who served as a first-team coach under Parkinson, insists that a position in the top two is still within touching distance for Sunderland and revealed the message that he delivered to the players ahead of the Burton game.
“The bottom line is that we’re still in a very good position in the league and we’re still within touching distance of the top two”, Taylor told his club’s official site.
“I said to the lads this morning that football moves fast, so we haven’t got time to feel sorry for ourselves or to let the emotions of what’s happened affect us.
“Whether I’m here or not, the end goal for this squad this season has to be promotion and that will not change.
“December is a big month for us and there is a lot of football to be played, starting with two big home games that we will aim to take six points from.”
Burton are struggling in League One, having picked up just ten points from their opening ten games, while they are winless on the road in the league.