Miyaichi came on in the 73rd minute with Arsenal nursing a one-goal lead and managed to impress the Gunners faithful with an encouraging display at both ends of the pitch.
The Japanese teenager did well to deny Gary Cahill from pulling Bolton even during stoppage time, leaving Wenger impressed by his defensive efforts.
"Ryo is a guy with heart. I don't think he played long enough and we were in a position where we had to defend more than we could attack," Wenger told the club's official website.
"But you could see straight away that his heart, his determination and his pace in the game are big assets."
Wenger alluded to potential Premier League appearances in December for his Japanese talent following an autumn spent mostly recovering from injury.
"He just had one day training yesterday with the group because he was injured. He worked a lot with the fitness coach," Wenger said.
When asked when Miyaichi would be ready, the French manager replied: "I believe he will be ready at Christmas."
Miyaichi joined Arsenal on a professional contract in January 2011 and was loaned out to Feyenoord for half a season.
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