Miyaichi is on-loan at Wigan from Arsenal.
"I was very pleased with his performance. I don't think he missed anything," Martinez said.
"I saw him as a real threat and he gives us a lot of penetration. Overall his contribution was very good and he is a player that is growing.
"He is still a young man but he will be a very important player for us potentially.
"He can play on the right or the left, he is decisive in one-on-ones and he is a really good outlet.
"He is one of those players who you really want to pay to watch. I was very pleased with his work-rate and his understanding."