"When we only had one point earlier in the season when everyone else had seven or eight, I was worried. But now we are back in the mix with games in hand," Poyet is quoted as saying by Soccerway.
"Of course, I try to do my best, but I'm not that worried. The situation is that if we keep looking at the rest and thinking other results were good for us today, then we are going to forget that we need to play ourselves, for 90 minutes every game.
"It doesn't matter who you play against or where you play, you need to make sure you do your bit because that's what you get paid for."
Sunderland are back in action on Wednesday night when they face Liverpool at Anfield.