The 35-year-old moved to Craven Cottage in September as a free agent and has featured in 10 of Fulham's Premier League fixtures since.
He also made a mark on his FA Cup bow for the Cottagers by scoring a tremendous equaliser for Martin Jol's side in the third round tie at home to Blackpool on Saturday.
Karagounis, who ended a five-year stay with Panathinaikos at the end of last season, wants to be as involved as often as he can be at Fulham.
"It was a great goal. It was important," he said of his goal against Blackpool. "I wish it was the winner. I was happy with the score. I want to use it as opportunity to thank the team.
"To score in front of the home fans was great but I want to show more and allow them thanks for letting me come here. I am here to play, I feel good and I want to help us as much as I can."
Fulham now face a replay against Championship outfit Blackpool with a trip to either West Ham or Manchester United the reward for progression into the fourth round.