Nwaneri did a superb job of replacing the injured Bukayo Saka on the right wing and scored in the 16th minute, but he had to be withdrawn at the interval before the Gunners conceded a penalty to drop two points in the title race.
"Really bad news, because I think we've lost him (Nwaneri). We had to take him off at halftime with some muscular issues," Arteta told the BBC.
Nwaneri's departure coincided with Arsenal losing their way against a Brighton side that struggled to create chances, and the result left the Gunners second in the table, five points adrift of Liverpool who have two games in hand.
"In the second half, we didn't really grab the game or dominate enough to have certain moments and be more of a threat in their half, but defensively we did not concede much," Arteta said.
"Today was not about fatigue, it was about the simple things that we have to do in ball possession to give chances and dominate the game in the right areas," the Spaniard added.
Arteta described the decision to award a penalty to Brighton for a clash of heads between Joao Pedro and Arsenal defender William Saliba as bizarre.
"We are really disappointed with the decision that leads to the goal because I have never seen something like this in my life. He (Saliba) touches the ball as well," Arteta said.