Goals from Yaya Sanogo - his first for the club - and Alexis Sanchez sealed Arsenal's progress into the UEFA Champions League knockout stages, but the result was soured by the calf problem sustained by Arteta.
With the likes of Danny Welbeck, Wojciech Szczesny, Jack Wilshere, Laurent Koscielny and Theo Walcott all missing the Group D clash at the Emirates Stadium through injury, another absentee is the last thing Wenger wanted.
Arteta was forced off midway through the second half, while Sanogo soon followed him with what appeared to be a hamstring problem.
And Wenger conceded that the initial prognosis for Arteta is not positive.
"That doesn't look good, it's a calf," he told Sky Sports.
"It's very difficult to take on the chin at the moment because we go into many games and you need everybody available.
"But I think Arteta will be out for a while."
Aside from their injury concerns, Wenger was pleased with his side's defensive performance after they were heavily criticised for their 2-1 Premier League defeat to Manchester United at the weekend.
"The focus was to defend well together," he said.
"We had a similar game to Saturday but we focused really well not to give any chances away and overall it was a committed game and we were better defensively.
"We are a team who likes to go forward and sometimes when we dominate the game we are victim of that and we forget to take precautions defensively.
"We learnt from other games and we've done that better."
Wenger also had words of praise for Alexis, whose 13th goal of the season was a precise curling effort from outside the penalty area.
"He has unbelievable fighting spirit and class as well," he said.
"He's a mixture of talent and desire and that's what you expect from top level players."
