The Magpies currently sit five points clear of the bottom three with three games remaining, but have played a game more than their nearest relegation rivals.
Taylor urged his team-mates to stick together to lift themselves out of trouble but acknowledged that they should expect criticism in the build-up to their next fixture against West Ham.
|9/1||Newcastle are 9/1 with Bet365 to be relegated from the Premier League
"In the dressing room, looking around everyone was devastated and realised the situation we are in. We have got to accept what's coming our way, and that's going to be the criticism this weekend leading up to the West Ham game.
"We have just got to put that to bed and focus on ourselves. Everybody is going to be criticising the team, the manager, everybody, but we have to stick together.
"We have heard those words a lot in the past six months, but that's vital now. The last three games are going to be like cup finals for us.
"We have to apologise, first and foremost, to the fans, for everybody who came here and watched the lads, and hold our hands up because we know we let them down.
"We are devastated with it, it wasn't acceptable and we all hold our hands up. It wasn't good enough. But we have to stick together and get on with it, and make sure next week we put this to bed and get the three points that we need. It's vital."