Poyet was understandably thrilled with his side's display, which landed them back-to-back Barclays Premier League wins for the first time since April last year and significantly boosted their chances of avoiding relegation.
He said: "What a league this is. We need to keep going.
"Before I said we needed to get safe somehow; now if we don't stay up, it would be a shame because we have done a terrific job until now.
"Now we are in a position where it is in our hands and we need to take it, so I am going to make sure that we do the right things from now until the end of the season."