Club and personal records both fell on an 'uncomfortable' evening for the Premier League leaders as they battled to control a game in which they were on the back foot early.
However, a penalty from Bukayo Saka, followed by a brace from Mikel Merino, saw them home as they stymied a Slavia side bent on pouring on the pressure.
Speaking about his side's victory, the manager said in his post-match press conference: "I am really happy. It is a really tough place to come. I told the boys to respect a team like this. (They are) super intense, very direct, man-to-man, so very short sequences of play with a lot of fouls.
"It was very difficult to get any fluency in the match, but we were patient and emotionally controlled with the way they set up.
"At the end, it looked comfortable, but it was not a comfortable match at all."
Slavia's fans created a tremendous atmosphere, as they so often do at home, and Arteta was pleased to see how his players had matured in these difficult situations.
He explained: "They haven't lost at home here all season, and they have that winning habit - that is very difficult to turn around.
"We understand that, and we knew the first 15-20 minutes there was going to be very little play. Then we had to change that and do different stuff. We did that, and the team showed maturity."
With Viktor Gyokeres missing through injury, and with the likes of Kai Havertz, Noni Madueke and Gabriel Jesus all out with long-term injuries, it left Arteta short up top. However, Mikel Merino stepped in as he did last season to score twice on the night, something his manager was delighted to see.
Arteta purred: "Mikel stepped up with two nice goals... He is just a joy to have. His versatility on the pitch with the things he can do, with his mindset he has, and today we were missing a lot of attacking players and we had to find a different solution and he comes in and scores two goals."
It was a historic night for the North London club. Not only did Max Dowman come on to become the youngest ever player to feature in a Champions League match, but the Arsenal defence also equalled a 122-year record after the win against Slavia, with their eighth-straight clean sheet. It is the first time since 1903 the Gunners have done that, and Arteta believes there is still more to come from his backline.
He added: "It was a long time ago, so it says how hard it is to achieve that. The most pleasing thing is not the record but the mindset of the players. They are in there talking about how to get better in one or two situations, so if we can do that, then that record will have a bigger meaning."
This Arsenal team can go ahead of the 1903 side on Saturday evening, when they take on Sunderland at the Stadium of Light.