The north London outfit faced an onslaught in the final moments of the game as they led 2-1, but held on to kick-start their group stage campaign with a win.
"You can't panic, we knew in the last 25 minutes they were going to throw some bodies up front and create some problems,” Arteta told the club's official website.
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"They missed a clear chance at the end but I am so glad to get the points, it is a brilliant way to start."
Arsenal came from behind to beat the reigning French champions, as Lukas Podolski and Gervinho cancelled out Younes Belhanda's opening goal.
And the Spaniard underlined the quality possessed by the Gunners' opponents, explaining that his team-mates expected the game to be difficult.
"We knew it was going to be tough, they were champions in France last year and that is no coincidence," Arteta continued.
"They work really hard, they have some talented players and scored the first one at home, which means it is always difficult to get back into the game.
"But we scored two brilliant goals and managed to get the result - it was vital for us to get the first three points away from home.”