Silva went down under a challenge from Burnley goalkeeper Nick Pope to win the spot-kick, from which Sergio Aguero broke the deadlock.
Burnley manager Sean Dyche was unimpressed by what he judged to be a theatrical tumble from Silva, who joined City from Monaco in July in a reported £43.5million deal agreed in May.
"It's minimal contact and to get that high off the floor with your arms above your head is almost a skill in itself," Dyche told a news conference.
"I was quite impressed actually, by how far he travelled. If I kick my kid in the garden, I don't think he'd fall like that."
But the Football Association has seemingly taken the opposite view to Dyche, confirming the Portugal international will face no further action.
"Manchester City's Bernardo Silva faces no further action for alleged simulation against Burnley FC on 21/10/17 after an FA panel review," read the FA's statement.
Silva has yet to experience defeat with City but warned fans the Premier League leaders' sparkling form is unlikely to go on unchecked.
He said: "We will try to keep it going and keep in first position. Manchester United lost points as well, so we are already five points ahead. We just have to keep doing our job.
"It's only the beginning, but it's always good when your opponents don't win. We have to stay focused on our games, but it's a good day for us.
"You cannot always win 7-0 or 7-2, or 6-1 or 5-0. Some games are more complicated than others, and the most important thing is to win the three points and then keep winning, winning, winning.
"When you get used to winning, everything is much easier -- the atmosphere, everything goes better and that's what we are trying to do."