Taylor admitted the atmosphere in the dressing room after the 6-0 home defeat by Liverpool on Saturday was dark, but he feels they must attempt to move on as quickly as possible if they are to avoid dropping deep into the relegation mire.
They travel to West Ham next Saturday only five points outside the bottom three with three games remaining but Aston Villa, who play Sunderland on Monday, and 18th placed Wigan have a game in hand.
"It's a sick feeling. At this moment in time, it feels like a family member has died, if I am being honest with you," Taylor said.
"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."