The Denmark striker was handed his first Arsenal start in 1,005 days by Arsene Wenger for Wednesday's visit of Steve Bruce's side and repaid the faith instantly with a goal after just 89 seconds of action.
Mesut Ozil netted early after the half-time break to seal a comfortable 2-0 scoreline.
Bendtner has previously expressed his desire to leave the Emirates Stadium having seen first-team opportunities dry up, although Bruce was one of several managers to baulk at the striker's wage demands in the close-season.
But Arteta hopes to see Bendtner remain in the Arsenal squad, and expects him to contribute further as they look to maintain their place at the top of the Premier League.
"He deserves it," the Spaniard said. "He has been working really hard. He got the chance and got a very good goal.
"The good thing is we can still rotate the squad and keep winning.
"The squad players can contribute and help the team be successful. Every member of the squad is important and Nicklas is no different.
"He is an Arsenal player and while he is here, he is 100 per cent here.
"I don't think he will be thinking of doing anything different because he likes playing here."
Arsenal's title credentials could come under scrutiny when they host Everton on Sunday, with the Merseyside club coming into the fixture on the back of defeating Manchester United at Old Trafford.
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