Semenyo struck in the 3-1 win.
He later said: "We have had two previous games here and we felt like we played well, but we didn't get the three points.
"We watched a couple of videos in the meetings in the week and we knew we could catch them out with quick free-kicks.
"Buzzing for (fellow goalscorer) Evanilson - he is going be a problem this year.
On his goal, he continued: "It felt wonderful. I wanted to create space and get a shot away.
"It rifled in the bottom corner, a great finish."
On his journey to the Premier League, Semenyo added: "It has been so important. All those loans and tough moments - it has been part of my joruney. Here I am loving the game and playing in the best league in the world.
"I'm grateful.
"The sky is the limit. We have such a good team and everyone is great. We just want to work hard and win games. We are going to cause a few problems this year."
Tavernier also said: "Something we have been working on this week is getting the ball in play as quick as possible.
"We knew if we got the press right we would create chances. That's what we did in the first half.
"Massive (three points). Coming back from two losses it was a big game for us today especially with it being a derby."