Finnan said: "I've never experienced anything like that before. I don't think there's a game I can remember like it in terms of atmosphere at any of my previous clubs.
"I really enjoyed it on Saturday, especially because of the result. It was a tough game and because it was my first derby I really didn't know what to expect. The lads and the gaffer give me a few tips to help me through it.
"After my injury, it was good of the gaffer to bring me into the team to face two of the Premiership's big guns. It was important to get 90 minutes under my belt against Tottenham and that set me up nicely for the Everton match.
"There was a lot of physical stuff going on in the early stages but you are always going to get that when those two teams meet. But we managed to find some space to play a bit of football.
"Everton had a few chances and Jerzy Dudek made a few good saves, but overall we were the better team."
Finnan was also delighted with the display of fellow new boy Harry Kewell and the continued excellence of Reds striker Michael Owen.
"It was great for Harry Kewell to create one goal and score the last. There's going to be a lot more to come from him. You can see that the longer he's here, the better he'll get," added Finnan.
"It was also nice for me to play a part in the first goal. You know when Michael Owen gets a chance he's going to take it."