The Gunners suffered their first continental defeat of the season in Italy, where Hakan Calhanoglu's spot kick on the stroke of half time made the difference in the league phase clash.
The Turkish midfielder stroked home from the spot after Mikel Merino was penalised for handball, as Mehdi Taremi flicked Calhanoglu's free kick onto the outstretched arm of the Spaniard.
Merino's hand was away from his body, but there was little that the former Real Sociedad man could have done in such close proximity to the ball; nevertheless, the referee pointed to the spot immediately.
Several minutes before conceding the game-defining penalty at that end, Merino was denied a spot kick of his own, despite being punched in the head by Inter goalkeeper Yann Sommer as both players challenged for a cross.
Arteta believes Arsenal were "very harshly done by" with penalty decisions
Speaking to TNT Sports at full time, Arteta only had positive words to say about his team's performance but hit out at both penalty decisions, claiming that Arsenal's denied penalty "100%" should have been given if the hosts' was.
"I am very proud of my players, the level of domination we had. We were very harshly done by in the sense that is obvious. Both penalties," the Spaniard said.
"If you are going to give a penalty, the other one has to be because he punches him in the head. There is no deflection, nothing you can do in the box, so can he get away from it. If he is going to give that the other has to be 100% a penalty."
Arsenal were enjoying the better of the action in the first half before Calhanoglu put the Serie A champions into the lead, but their familiar problems reared their ugly heads time and time again in the second 45.
With Martin Odegaard being held back after his return from an ankle injury, there was little creativity among the Arsenal players, who could not penetrate the Inter defence through the middle and resorted to a plethora of unsuccessful at San Siro.
Arteta: 'If Arsenal play like that against Chelsea, we will win'
The Gunners sent in a staggering 46 deliveries and also had 13 corners on the evening, but not a single one led to anything meaningful, and only four of their 20 shots were on target.
Ethan Nwaneri was at least a bright spark off the bench, while Odegaard made his return from almost two months out towards the end, but the Norway international could not provide a moment of magic in the short time that remained.
A challenging trip to Chelsea now awaits for Sunday's Premier League battle, but a defiant Arteta insisted that his team can prevail at Stamford Bridge if they perform in the same manner as they did at San Siro.
"We should have scored a couple at least but the way the team played, that was us at least. Every decision in the box makes a difference. The way we played tonight, the team can go to Chelsea and win," Arteta added.
Arsenal's first European defeat of the season leaves them 12th the Champions League table, albeit just two points adrift of the top eight and a guaranteed spot in the knockout phase.