Morocco forward Ziyech bagged the winner for Chelsea with a cool finish from Timo Werner’s pass.
As well as a second successive FA Cup final appearance, Chelsea also have a Champions League semi-final to look forward to.
The Blues will face Real Madrid over two legs after winning 2-1 on aggregate in the quarter-final against Porto on Tuesday.
“It was a perfect week and we can enjoy that. Now it’s a special end to the season if you see what we are still playing for,” Ziyech said.
“All the ways are open and everybody is excited about it and we cannot wait to play those games.”
Ziyech was Chelsea’s stand-out performer against City after coming into the team as one of three changes from the second leg against Porto.
The 28-year-old came off in the closing moments at Wembley and admitted he was anxious watching his team-mates hold onto their lead.
“Those moments are always nervous from the stands,” Ziyech said.
“I tried to stay calm but sometimes it’s difficult! In the end everybody did well, we killed the game and we kept a clean sheet as well.
“Timo (Werner) did a good run into the space (for the goal), I made my run, it was a good delivery and I put it in easy.
“You always have to have that feeling before the game that you want to score.
“It feels good to be in the final. Everybody is happy. We did a good job, especially in the first half.
“The second half was a little bit difficult to close all the spaces, but we scored the one goal that we needed. It was enough.”