Villas-Boas broke the news of the kidnapping to Mikel on Saturday, 24 hours before Chelsea's opening Barclays Premier League game of the season at Stoke.
The former Porto boss acknowledged the response of Mikel, who has also put his hand up for Sunday's clash with West Brom, had demonstrated "amazing mental toughness".
He added: "I just have to go with the word my player gives to me and for the game against Stoke, Mikel felt well to play.
"People go through big disappointments and personal things in their lives and they can still be able to play because they feel well on the pitch, to avoid the things that are running in their personal lives and they can focus on on different things.
"Mikel made himself available for training and selection so I will just judge it like that.
"Players react in different ways.
"Some players want straight away to go back to their families, others prefer to be like this and live on day by day, not because they think they are distanced from where it is happening, but it's their choice."
Villas-Boas admitted it had been "difficult" breaking the news to Mikel but would not be drawn on further discussions between the pair.
"I wouldn't like to go into it - it's a pretty sensitive situation and pretty traumatic," he said. "Hopefully, he can get this thing solved as soon as possible that's what we hope for."
Source: PA
Source: PA