"I was delighted to be part of that," the Senegal fullback told the Evening Chronicle. "To win 2-0, keep a clean sheet and beat Sunderland was a very good game for us.
"It was good for the crowd and everybody in the city.
"It means everybody is happy because you know you can't lose these games. It's a big derby and it's great for the whole club."
Speaking on his gesture to hand over his jersey, Beye added: "It was to say thank you to the crowd.
"I gave it to a little child and it's important to do this sometimes.
"We use 38 shirts each season, so it's good to give one to a young fan.
"Once I'd given it away though I realised how cold the weather was in Newcastle!
"But I enjoyed playing in this game so much.
"It was my first time and hopefully it isn't the last time."