After seeing a video replay of the incident, Schar said he had no memory of it.
"It looks awful. I can't remember anything," he told Swiss newspaper Blick. "I was out for a few seconds. My skull is still humming. I've got neck ache and a bruise on my forehead but it was worth it."
Schar has since been ruled out of Switzerland's qualifier against Denmark later on Tuesday.
"I really wanted to play and, as always, give everything to the team and Switzerland," he said in a statement on the Swiss FA website https://www.football.ch/SFV/Nationalteams/A-Team/News/schweizer-a-nationalteam-gegen-daenemark-ohne-fabian-schaer.aspx confirming he would be rested.
Britain-based brain injury charity Headway called on European soccer's governing body (UEFA) to investigate the incident.
Protecting players from concussion is part of a growing debate in sport and global players' union FIFPro earlier this month criticised how professional football deals with concussion while pointing out failings in current protocols.
"How many more players will have their careers and ... lives and long-term health put at risk by the sport's inability to follow its own protocols?" the BBC quoted Headway Chief executive Peter McCabe as saying.
"Put simply, the decision to allow Fabian Schar to return to the field of play after suffering a clear concussion was not only incredibly dangerous, but also a clear dereliction of duty.
"The player's comments after the match are also deeply disturbing and again show the lack of awareness and understanding among players. UEFA must immediately launch an investigation into the incident."
(Reporting by Simon Jennings in Bengaluru; Editing by Peter Rutherford)
