Arshavin made the most of a mistake by Swansea keeper Michel Vorm, who threw a clearance against team-mate Angel Rangel to allow the Russian to score just before half time
Wenger said: "Mertesacker was calm and composed. He leads the line well and of course needs time to adapt to the pace of the game in this country but I was pleased with him.
“We just wanted to get over the line and not make a mistake”
"Arteta played very well overall, especially in the first half. In the second half it was more difficult for him but you could see he will bring something to us technically in a team that likes to play the way we play."
Arteta added: "It was important to get the three points and we've done it. It was important to forget about what happened two weeks ago [the 8-2 defeat against Manchester United] and now we have a big Champions League game on Tuesday [Borussia Dortmund] and let's focus on that now.
"It's been good. We had the chances early on to get the game in our hands and we didn't take them and then it was a bit harder.
"But credit to Swansea, they played really well they have some good players and are brave to get the ball at the back. It's not easy to come here but they were brave and showed some confidence. It wasn't easy but I'm glad for the debuts and glad for the three points."
He said: "He brought us something when he came on. He was mobile, dynamic and overall did well."
Wenger was relieved to see Arsenal secure their first league win, saying: "It was vital for us to win this game. We started well but slowly the nerves took over and we played with the handbrake on and [were] restricted in the second half.
"It is not often you see us pass the ball back to our goalkeeper when we are on the halfway line but you could see the nerves in the second half. We just wanted to get over the line and not make a mistake. If you make a mistake, you know you then don't win a game it is vital to win."
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