Manchester City had earlier slumped to a 2-0 defeat by Manchester United, giving Arsenal the opportunity to open up a nine-point gap, but they could not find the back of the net against Forest.
"We came here to win the game, and again, we haven't managed to do that, and credit to them, the manner that they are organised," Arteta told broadcaster TNT.
"When you have the four big chances that we have with (Gabriel) Martinelli, an open goal, Declan Rice, Mikel Merino, Bukayo Saka, at the end, you have to find the margin to win the game, because again, we haven't conceded a single shot on target."
Arsenal lead the standings on 50 points, seven ahead of Manchester City and third-placed Aston Villa, who play Everton on Sunday.
Arteta's side were also denied a late penalty when the ball struck the arm of Forest defender Ola Aina, but a VAR review found that no infringement had taken place.
"You have to produce that moment. We've created certain moments, but credit to them as well because they are very well-organised and they disrupt your momentum in clever ways as well all the time," Arteta said.
Forest manager Sean Dyche was very happy with his side's performance against the league leaders.
"I would be very, very disappointed if that (penalty) was given, and I would be unbelievably delighted if that was given for us," he told the BBC.
Forest are 17th on 22 points, five points clear of the relegation zone.
"We've got to be realistic about where we are now. There's a lot of good work done now, and a lot of good work out there today, but there is more to come," Dyche said.