Boss Mikel Arteta rues early goals making life difficult for Arsenal
Arsenal conceded 57 seconds after kick-off when Andreas Pereira (27) pounced on a loose back pass and fired the visitors ahead even before fans had taken their seats.
The goal made Arsenal the first team in Premier League history to concede a first-minute goal three times in a calendar year.
"We have this situation a thousand times in football. We gave the ball away in a really dangerous area and it was a really cool finish," Arteta told the BBC.
"Right from the beginning, we gave an incredible goal away. You make life really difficult for yourself. But the team reacted really well.
"We dominated the game and created countless chances and should have scored five, six, seven goals easily. When you've done the most difficult thing - get back ahead against a well organised team - you have to defend your box from one corner."
After failing to find the net in the first half, Arteta made changes in the second and he was happy to see substitutes Fabio Vieira (23) and Eddie Nketiah (24) dragging Arsenal back into the game.
Vieira first won the penalty for Bukayo Saka (21) to level the score at 1-1 before providing the assist for Nketiah to make it 2-1.
"Fabio was involved in everything we created and I am really happy with that. To see players with the ability to make and take chances with quality," Arteta said.
"The same with Eddie (Nketiah). It is my fault that Fabio has not played more and today he gave me reasons to play him more."
However, Fulham scored a late equaliser through Joao Palhinha (28) from a corner despite going down to 10 men, which left Arteta fuming as Arsenal dropped two points and failed to move top of the standings.
"We have to show another level of commitment and desire - 'over my dead body'. With 10 men, you cannot concede a goal," he said.
"It's the only chance they have and you get punished. Yet still you get another two chances and don't score, that's the story of the game.
"(For) the amount of things we did to merit to win the game comfortably, we end up with one point."