Ireland won 2-0 thanks to Troy Parrott's double, with Ronaldo seeing red for an elbow on Dara O'Shea.
"He complimented me for putting pressure on the referee," said Hallgrimsson when asked about their touchline exchange, which ended with a handshake.
"It was his action on the pitch that cost him the red card. It had nothing to do with me - unless I got into his head."
Asked if he spoke to Ronaldo after the game, Hallgrimsson added: "No, I think we spoke enough when he came off.
"There was nothing to speak about. This was just a moment of a little silliness from him, I would say."
In contrast, Portugal coach Roberto Martinez insisted: "The red card is just a captain that has never been sent off before in 226 games - I think that just deserves credit - and today, I thought it was a bit harsh because he cares about the team.
"He was 60 minutes or 58 minutes in the box being grabbed, being pulled, being pushed and obviously when he tries to get away from the defender.
"I think the action looks worse than what it actually is, I don't think it's an elbow, I think it's a full body, but from where the camera is, it looks like an elbow. But we accept it.
"The only thing that leaves a bitter taste in my mouth is at the press conference yesterday, your coach was talking about the aspect of the referees being influenced, and then a big centre-half falls on the floor so dramatically at the turn of Cristiano's body."