The Gunners came from behind to earn a 2-1 Europa League victory in Austria on Thursday to open their Group B campaign.
It was far from plain sailing, as a quiet first half was followed up by a mistake from goalkeeper Bernd Leno which allowed Taxiarchis Fountas to give the hosts a 51st-minute lead.
But David Luiz's header levelled the contest before Arsenal captain Pierre-Emerick Aubameyang tapped in the winner with 16 minutes remaining.
Arteta was quick to praise Partey following the victory, with the Gunners' £45 million signing from Atletico Madrid playing the full 90 minutes and earning a 7.2 FC Rating on his first Arsenal start.
"Partey looked really solid and really comfortable," Arteta said of the Ghana international, who had made his debut as a late substitute in the weekend defeat at Manchester City.
"He held midfield by himself in the second half when we were more open. He was fantastic tonight and there is much more to come.
"We know with the price we paid for him he is going to have a lot of people looking to him."
After Leno passed the ball to Rapid's Ercan Kara from inside his own six-yard box in the build-up to the first goal, Arteta acknowledged there is a balance that needs to be struck when it comes to his aim of playing the ball out from the back.
"It's part of our game," he said. "We need to understand when we can do that and when we should kick the ball into the stands.
"They will understand better and better the type of balls we have to play in those areas and to who in relation to the pressure that is coming.
"We knew it was going to be a difficult match. We made it harder in the beginning with the goal we conceded.
"But I really like the reaction and the second goal was fantastic."