The draw was scheduled to be broadcast live on Twitter at 1600 local time, but was delayed by nearly two hours due to technical problems before being shown in a pre-recorded video.
"We're sorry for the issues that led to the delay of today's Round Five draw," Twitter UK said in a statement.
"We would also like to apologise to the thousands of supporters who had been patiently awaiting news of who their team would be playing."
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Arsenal host London rivals West Ham United and Premier League leaders Manchester City are at Leicester City in a repeat of their match at the same stage of the competition in 2013-14.
Manchester City won that game 3-1 and went on to lift the trophy.
Champions Chelsea welcome Bournemouth in the other quarter-final with all matches to be played in the week commencing Dec. 18.
The English Football League (EFL) said a number of technical issues had affected the draw.
"The EFL has received an apology from Twitter UK for the delay which is believed to have occurred as a result of a faulty encoder," the organisers said.
"The EFL has requested a full explanation into the events that led to this afternoon's unacceptable delay."
(Writing by Simon Jennings in Bengaluru, Editing by Ed Osmond)
