Johnson was pivotal in Sunderland's cup successes over the last week, helping them overcome Carlisle in the FA Cup third round before winning the penalty that sealed a 2-1 win over Manchester United in the Capital One Cup semi-final first-leg.
And Poyet hopes he can take that form into the league and show why the club paid £10m for the former Manchester City midfielder in August 2012.
Speaking ahead of Saturday's clash with fellow strugglers Fulham, Poyet said: "When you have got a player like Adam who is on good form the chance that you will stay in the Premier League is massive.
"Adam has started the year fantastically and he made my day the other day so I am looking forward to seeing him stay on that level.
"I have seen him happier and more relaxed and really going for it. When we told him what we wanted him to do we didn't know if it was going to be possible, but he gave us all we wanted to see."
The Uruguayan admits he has been puzzled by the contrasting results in the cups and league, adding: "I will try to make them think we're playing in the cup on Saturday.
"I'm looking for the difference if there is one. I think sometimes when you're playing for points you are in a situation where you sometimes unconsciously think a point away from home can be good enough.
"That way of forcing the game for the last 20 or 30 minutes because you want to win the game is different in the cup, because you need to win. Can we create that mentality in the league? We'll try.
"We know that Fulham have been starting games fantastically so we will have to cope with that and impose our game.
"The cup can go away quickly. Everyone thinks about it but then you play one more game and you can be out. So we need to concentrate on every game as it comes and now the most important, massive game is Fulham."