The Irishman had been strongly linked with a summer move to Premiership rivals Blackburn and Tottenham Hotspur, but the 28-year-old is now able to concentrate on proving his worth to Rafael Benitez.
Finnan said: "People have different opinions on whether I should be playing or not. That's up to them. I've not worried too much about the speculation.
"There's been a lot of talk about a number of players leaving. I'm just glad the transfer window is closed now because no-one will leave until January.
"I've never felt that worried about it, to be honest. I didn't speak to other clubs, but if Liverpool had agreed to sell me there would be nothing I could do about it. In football, if you're told to go, you go.
"There are always going to be 10 or 11 players who aren't playing every week, and they won't be happy.
"Apart from two or three, I don't think anyone will be playing every game. You've just got to get your head down and hope you'll get your fair share of matches during the season, especially the big ones.
"To score my first goal, especially at Anfield, is a great feeling. I'm enjoying playing right midfield. First and foremost I'm a full-back and that's where I'd like to play. But as long as I'm playing I'm happy.
"It was a good performance. It was exactly what we needed after a couple of defeats."