"Rob takes a lot of credit," said Ferguson. "It helps in terms of him showing some humility towards the game. That is the most important thing.
"It is good he has done it. It presents him in a different light. It shows he has character and is big enough to do it."
But speaking after Saturday's game, furious Bolton boss Gary Megson described the penalty decision as "nonsense" and said he was not interested in an apology.
"I don't want him to ring me up," said Megson. "I would have more respect from him if he just holds his hands up and says he was wrong."
It is unknown in what manner Styles contacted Bolton on Monday or who he got in touch with.
Styles drew criticism in some quarters for not publicly admitting his mistake on television immediately after the game.
But contrary to some reports, he was not restricted by PGMO guidelines from doing so.
"Referees, should they so wish, have the opportunity to conduct post-match media interviews, after 30 minutes' 'cool-down' time, to clarify any point of law," said a spokesman for PGMO, the body responsible for top referees.
But the PGMO does not want a situation where referees regularly face 'trial by television'.
It stresses that it works closely with officials in analysing their performances after each match in order to maintain and raise standards.
Officials who make mistakes often miss out on refereeing a Premier League match the following weekend.
But the PGMO insists that referees are not automatically demoted when they make a high-profile mistake, merely that they are being taken out of the spotlight for a week or so.
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