The young keeper excelled as the Blues progressed via a penalty shoot-out, saving four spot kicks to render an earlier mistake which led to the Inter goal meaningless.
And the manager was delighted with the 20-year-old’s match-winning display in the shoot-out.
“I thought he was wonderful,” said Davies.
“It was his mistake for the goal, but he more than made up for it.
“He’s going to make mistakes because we ask him to play out from the back all the time and he is magnificent at it.
“I ask him to do that so it’s not his fault and overall he had a really good day at the office.”
READ: City 1-1 Inter Milan
READ: Grimshaw delighted with spot-kick redemption
City responded to Inter’s early goal through a Lukas Nmecha penalty but a second proved elusive.
It was not for the want of trying, with the young Blues creating a host of chances before half-time, but in Inter they came up against a well-drilled, physically imposing five-man defence.
Presenting City with a different challenge, Davies was quick to acknowledge the Italian’s efforts and was equally as impressed with his side's performance as he was the result.
“To get to the quarter-final of any competition is great, but especially in Europe,” explained the manager.
“I thought we controlled the game throughout, that’s partly because they wanted to play on the counter, but I’m really proud of the lads and the work they put in against tough, well organised opposition.
“We knew that if we gave them a cheap goal it was going to be a tough game. That proved to be the case and they were a different test for us.
“They sat off, they passed well, they had a good target man and good players around him so they caused us problems at times.”
City now face the prospect of an all English quarter-final tie, where they will face Liverpool or Manchester United and it’s a challenge Davies is keen to embrace.
“Either tie will be great,” he added. “But most people will be wanting a Manchester derby.
“We know a enough about them and they know a lot about us as well, so whoever we face, it will make for a really exciting fixture.”