The Black Cats claimed a 0-0 draw at Leicester for their first clean sheet since being thumped 8-0 at St Mary's last month.
Kasper Schmeichel denied Steven Fletcher and Adam Johnson in the best chances of a tight game at the King Power Stadium.
And Poyet believes his side have now healed the wounds from their south coast nightmare.
"I think we are back to normal
I needed to think about what happened three or four weeks ago and we needed to get back to basics," he said.
"That day (Southampton) was a terrible day, it was something unique but it creates doubt in the players' minds and in the next game we made two massive mistakes (against Arsenal).
"We play Chelsea, Manchester City and Liverpool next so in two weeks' time I'll let you know if we can do the same
It's a decent day."
The Foxes have not scored in 500 minutes - since their 2-2 draw with Burnley last month - after another blank.
Leonardo Ulloa failed to make an impact again but Riyad Mahrez twice went close and Matty James was denied by Costel Pantilimon.
Mahrez also saw a second-half penalty claim ignored - a decision Poyet admitted Sunderland were lucky to get away with.
"On another day it goes against you, today we were lucky it didn't," he added.
Foxes boss Nigel Pearson, though, insisted there is no anxiety from his side about their goalless streak
"Not that I'm aware of, maybe around the stadium but not necessarily among the players," he said.
"We got the point, we have played pretty well and we worked the goalkeeper
We got criticised at Southampton for not having any shots on target but we worked the goalkeeper today and we were the better side.
"On another day we would probably win the game."
The point lifted the Foxes out of the bottom three in the Barclays Premier League but they are winless in their last seven games.
"If the players play in that fashion we will be fine
We created chances and things didn't quite go our way," said Pearson.
"I was pretty pleased with the performance and it was only a second clean sheet of the season
The margins remain small but I am pleased with the performance."
Source : PA
Source: PA