The 21-year-old French international, who spent the last three seasons away from Arsenal on loan, frustrated attempt after attempt by the Eagles to create opportunities and was given Sky Sport's man of the match award.
The Gunners walked away with all three points at Selhurst Park thanks to a first-half Gabriel Martinelli header and a late Marc Guehi own goal.
"You don't really see that," said Arteta.
"At 21 years old in the Premier League, against these physical players and resolve the situation the way he's done it, with that composure, that calmness and that presence. Big credit to the boy."
Saliba admitted he was delighted to finally make his proper Arsenal bow.
"It's been a long time I've waited for this moment, I'm so happy to start my first game with a win and a clean sheet. It's never easy, you have to give your maximum and it was good," he told Sky Sports.
"It's the first game, it's important to win for the confidence and to start the season well."
Arteta also admitted that much more was required from his attackers.
"We need to be more ruthless in front of goal," Arteta said.
"We had a situation to finish them better, even in the second half, but that's something that has to come. We haven't scored a lot of goals, we lacked that real edge."
Still, the Gunners boss was pleased with his squad's overall effort, a marked improvement over their 2-0 loss to Brentford at the start of last season.
Martinelli nearly put Arsenal on the scoresheet early in the first half when the ball landed at his feet the edge of the six-yard box, but the Brazilian's effort sailed well wide across the face of goal.
Redemption followed after he rose highest to nod in the opener in front of a crowded goal in the 20th minute.
The game was decided when Bukayo Saka's 85th-minute cross connected with the head of the unfortunate Guehi.
Arteta was ultimately delighted to walk away winners under the intimidating Friday night lights at Selhurst Park, looking a very different side to the one who fell to the Eagles 3-0 in their last meeting in South London.
"I'm really pleased," he added. "Three points and a clean sheet against a really difficult opponent and a really tough place when they have the people going, and as we expected we were going to have tough periods during the match.
"You don't win here without resilience. We experienced that last season, we started in a really different way than we did last season when we were here.
"It's building that mentality and finding a way to go through those moments, maintain clean sheets in this league, is going to be vital to our success so hopefully that will breed some confidence as well in the team."