Despite giving away the foul, the 27-year-old is hoping to learn from his mistake.
"We deserved to win," said Richardson. "It was a silly mistake from me to give the free kick away and it led to their goal.
"It was a free kick but before that we should have had a free kick for [a foul on] Karagounis but the referee didn't see it. It was a bit of frustration from me.
"A player of my experience should have dealt with that situation quicker. I'll learn from that and hopefully we can win the next game."
Fulham currently lie ninth in the Premier League.