The west London side went into the clash with just one win in 12 matches, leading to a slip into the bottom half of the Premier League table in 13th place.
However, goals from Alex Kacaniklic and Dimitar Berbatov earned Martin Jol's side a much-needed three points, which Karagounis hailed as integral for the club.
|JOL HAPPY WITH WIN AFTER NYE DISTRACTIONS
|7/1||Fulham are 7/1 with Paddy Power to defeat Blackpool 2-0 at home in the FA Cup this weekend
"We must leave that behind us now because we started the New Year with a massive victory away from home which helps give our confidence a boost given the results from the previous matches," Karagounis told the club's official website.
"I think that we can now take this forward in the next games that we play, starting with Saturday's FA Cup match against Blackpool.
"The result against West Brom can help us move forward now with greater confidence because the team doesn't deserve to be in its current league position but higher up - as we were at the start of the season.
"We want to finish as high as possible in the Premier League and to progress as far as we can in the FA Cup. If we have a chance to win it, then why not?
"If we keep our focus on the game we are about to play, it shows that we will always give each fixture our full concentration which in the long run will be better for everyone and the team."