The two sides drew 3-3 at Anfield on Wednesday evening.
The Gunners looked set for three vital points at Anfield as they led 3-2 at the death, before a last minute Joe Allen strike rescued a point for Jurgen Klopp’s side.
It was highly disappointing for Arsenal after they had twice come back from a goal down to lead 3-2 in the game.
And Giroud, who bagged two goals on the evening, says he hopes his side don’t come to regret the two dropped points at the end of the season.
“My first feeling is disappointment but we have shown some character to come back from 1-0 and 2-1 down,” he told BT Sport.
"Hopefully, we are not going to have to regret this goal at the end of the championship.”
“It is still a draw, they've done well at the end of the game and pushed a lot. It's a good performance but we could have done better."
The good news for Arsenal is that despite dropping two points at Anfield, they still managed to stay top of the table.
Their main title rivals, Manchester City, could only manage a point at home to Everton, meaning they are now three points behind the Gunners in third place.
Leicester City did however manage to win at Tottenham to put them joint top, and Arsene Wenger’s side will be hoping to shake them off at some point as the season progresses.