Johnson settled an entertaining contest in the 90th minute, volleying home to condemn Newcastle United to a 1-0 defeat at St James' Park on Sunday.
But he was being lined up to be withdrawn not long before, only for Poyet to have a change of heart at the last moment.
The Uruguayan said: "I was going to take Adam Johnson off. For some reason, I didn't. Don't ask me why because I do not know.
"Luckily enough, Johnno went on to score the winning goal - and that was fantastic for us.
"It was only at the last moment we changed it and brought Connor [Wickham] off. You can say it's lucky, but we have not had much of that this year so I'll take it."
The victory was Sunderland's fourth in a row in the derby - a club record run of wins.
Poyet added: "It was a special moment for us, a special moment for the club. We were able to continue this winning run against Newcastle, which is great for us."
The 47-year-old felt Johnson's goal was just reward, with Sunderland having spurned a series of good chances.
"I think we were better in terms of creating chances," he said. "I thought we had the clearer chances.
"So many things happened even before the goal. In terms of chances, we were better.
"It was a close game, but I think we created enough to score. We always talk about confidence and now confidence should be high."