Crystal Palace winger Eze was allowed to sit in the directors' box at Loftus Road to watch his former club despite the current ban on fans and the national lockdown.
The Football Association is understood to be looking into the incident which seems to be the latest in a string of footballers breaching Covid-19 protocols.
"We know the situation that society is facing in this country, we are all very aware of it," said Warburton at a pre-match press conference.
"QPR as a club have stringent protocols in place that we apply very strongly to every single player and staff member.
"On this occasion we should have declined the request. It's as simple as that. We made the error.
"Eberechi is an outstanding character. I can't speak highly enough of him. He made a request, we should have said no.
"On this rare occasion we have made a mistake, it's as plain and simple as that. It will not happen again."
Eze, who joined Palace from Rangers for around £20million in the summer, was pictured not wearing a mask as he sat in the stands.
Palace have so far declined to comment but Eagles boss Roy Hodgson said last week that no further breaches of Government guidelines by his players will be accepted after Luka Milivojevic broke the rules on New Year's Eve.
Palace captain Milivojevic issued an apology after his household mixed with Fulham forward Aleksandar Mitrovic and his family.
There were further breaches of the regulations over the festive period involving Tottenham, West Ham and Manchester City players.