The Giallorossi enjoyed a good start after taking the lead in the fifth minute through Pablo Osvaldo, but Lazio equalised through Hernanes from the penalty spot five minutes into the second half, after Kjaer brought Cristian Brocchi down in the box.
The Dane saw red for that challenge, and playing a man down, Roma eventually succumbed to Lazio when Miroslav Klose netted a stoppage time winner.
And despite revealing the pain of defeat was too much to bear for him in the days that followed, Kjaer has put his hand up and admitted to making an error in that match.
"Perhaps it was a foul," Kjaer told Sky Sport Italia. "I reached out and he [Brocchi] threw himself to the ground.
"The referee sent me off and gave them a penalty, and that was the end of the game for us.
"It was not nice for me, and the subsequent days were hard. I felt sick and I was really sorry for the fans, but now I know better."
And Kjaer is aware that Roma must not get their season back on track with a positive result against Palermo this Sunday.
"The team must look forward now and hopefully they will be able to beat Palermo."
Roma have had an inconsistent start to the season, and currently lie 12th in the Serie A standings.