The 29-year-old left-back was dismissed in the 73rd minute of the Group A encounter at the Amsterdam ArenA in Amsterdam.
Izaguirre picked up two yellow cards and failed to complete the entire 90 minutes, as Celtic played out a 2-2 draw with their hosts Ajax.
The Honduras international has revealed to The Scottish Sun that after the match he apologised to his Celtic teammates for his dismissal.
“I am very disappointed with my red card,” Izaguirre told The Scottish Sun. “I need to take responsibility for the dropped points.
“I was worried I had let the team down leaving them with ten men. I said sorry to the team. It was a big game and we needed to keep 11 men on the field.
“They accepted my apology and were fine with it because it happens and now I need to be focused and 100 per cent for the next games.”
Celtic took the lead against Ajax in Amsterdam as early as the eighth minute through Nir Bitton, but Viktor Fischer restored parity for the hosts with a well-struck shot on 24 minutes.
Mikael Lustig headed home for the Hoops three minutes before the half-time interval, but Lasse Schone made it 2-2 with a free kick in the 84th minute.