Sexton revealed he had apologised to Farrell and it was "time to move on," with the head coach dismissing the incident as "a storm in a teacup."
Sexton shook his head staring up at the coaches at the Stade de France when he was replaced by Ross Byrne with just over 10 minutes remaining of the 35-27 loss which dashed Irish hopes of lifting the Six Nations trophy.
Sexton's behaviour was criticised by two former captains, Brian O'Driscoll and Keith Wood.
Sexton said his reaction was down to being unhappy with his own and the team's performance.
"I was really disappointed in myself to a certain extent. It was heat of the moment and in the biggest game I have played as captain," he said.
"Yes it was a low point to be taken off but I reacted in a bad way, that is all I can say. I spoke to Andy after the game and on Sunday when I apologised.
"I am not going to sit here and apologise to the whole world. It should not have happened it did," he said.
Sexton -- whose form since being named World Player of the Year in 2018 has been affected by several injuries -- said he and Farrell understood each other.
"You move on. It is not the first time I have apologised and won't be the last," he said.
"We have a good relationship."
Farrell -- who appointed Sexton captain when he took over after the 2019 World Cup as predecessor Rory Best had retired -- said telling off the Leinster playmaker would be counter-productive.
"It was 100 percent a storm in a tea cup. Johnny is a passionate guy and it is a reason we all love him as a player for how long he has been at the top of the Irish game," said Farrell after the squad for the Autumn Nations Cup had been unveiled
"I don't feel undermined and neither do the team.
"We need Johnny to be himself and there is always going to be learnings along the way but you are not going to change overnight a person who has been at the top because of the intent and attitude he has got."
Farrell -- who is in his first national head coach role after being an assistant to both Stuart Lancaster with England and then Ireland under Joe Schmidt -- said he and Sexton enjoy a good working relationship.
"Me and Johnny are always talking together. We speak most days," said the 45-year-old former rugby league great.
"We always discuss everything that goes on -- we are always discussing his individual game, his captaincy, we are always learning together."
Sexton for his part denies that wearing the captain's armband is too heavy a burden for him.
"No, I love being captain. When Andy asked me to do it, it was the biggest honour of my career probably and I am incredibly proud to do it," he said.
"I am trying to get better in the role, and always seek out opinions and talk to the lads and the management to see if I am doing a good enough job."