The result at the New Den comes as a welcome respite for Coyle after last weekend's Premier League defeat to Wigan left them languishing in 19th place, and he was quick to single out Miyaichi for individual praise.
"His second-half performance against Wigan last week was terrific, and from that moment there was no doubt he was going to start today," Coyle said.
"He showed what a talent he is. There's other stuff he can learn, but he's brave and tough - he stood up to some of the treatment he got today - and he always plays with a smile on his face, which I absolutely love."
Coyle revealed he has been a long-term admirer of the precocious 19-year-old and was determined to bring him in on loan from Arsenal.
"First and foremost I am a football fan and I want to be excited by some of the players I've got in my team, and Ryo Miyaichi certainly does that," he said.
"In football terms he is a baby, a kid. I saw when Arsenal brought him in and then watched him on loan at Feyenoord last year, and he always caught my eye.
"I spoke to Arsene a few times about him and did everything I could to get him to the football club."
Miyaichi opened the scoring for Bolton in the fourth minute after a quick free-kick from Sam Ricketts and the tie was sealed when David Ngog scored a long-range effort in the second half.
The performance pleased Coyle who was expecting a tough match.
"I know from both my playing and coaching days how difficult any cup tie can be," he said.
"I've been an underdog many, many times. I think we started well. It probably took Millwall 15 or 20 minutes to get into the game, but when they did they had a few corners and a bit of pressure.
"We stood up to what was always going to be a difficult test. We defended well - Tim Ream had a terrific debut."
Millwall boss Kenny Jackett questioned the decision that led to the opening goal and felt his side's lack of a cutting edge cost them.
"Whether it was a free-kick or not is debatable but they took it quick and to give a Premier League side a start like that is disappointing and gave them something to hold onto - basically after that their game plan was to sit deep," he said.
"We had a lot of good possession and some good moves without being able to get that goal. There were some key moments - their full-back (Gretar Steinsson) nearly scoring an own goal in the first half and then a good double-save by the goalkeeper.
"We need one of those moments to break for us because that would have obviously got us back into the game."
Jackett wants his team to learn from the game but insisted his players can be proud of their efforts.
"They have got a good ball retention about them and the first pass is always very safe and it is something we have to learn from," he said.
"It was a good run in the FA Cup and we haven't disgraced ourselves today but we have to look forward very quickly now."
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