Bernardo Silva pulled one back for the hosts in the second half, but they fell short of a comeback and Arteta - who took charge of the team due to a touchline ban for Pep Guardiola - acknowledged that it was a disappointing result for his side.
"We saw two very different halves. We conceded many counter-attacks and at this level you get punished. In the second half we dominated and played in the opponents' half and created many chances," he told BT Sport.
"I still believed we could do it. We reacted really well. On another day we could have come back. If you give cheap goals away it is difficult. The subs affected the game but sometimes it is too late.
"I was told there were two penalties in the game but I did not see clearly. It is disappointing. We are usually strong at home. Now you have to go and win away from home."
The defeat saw City become the first English team in Champions League history to lose four consecutive matches in the competition.