The teams drew 2-2 after Chelsea, who conceded two early goals, launched a strong second-half fightback to recover from two goals down and earn a replay.
Benitez said he had waited before the match to greet Ferguson but that the Scot, with whom he traded many jibes in his days as manager of United's arch rivals Liverpool, had walked past him.
"I was waiting at the beginning," the Spaniard told a news conference.
"I have education because I know a lot of people are watching so I know what you have to do."
Ferguson was fuming after United's controversial Champions League exit to Real Madrid on Tuesday and did not give a post-match news conference following the Chelsea game, spurning the opportunity to explain his take on the Benitez incident.
The Chelsea manager urged the gathered reporters to tackle Ferguson over the matter.
"Ask him, if you are brave enough," he said.
Asked why he had not shaken hands with Ferguson after the game, Benitez replied: "At end of game I was celebrating with my players."
Ferguson and Benitez used to regularly indulge in mind games and they picked up where they had left off when the Spaniard was installed as Chelsea's interim manager in November.
In 2009 Benitez infamously produced a hand-written list to back up his view that Ferguson was never punished for verbally abusing match officials and he once joked the Scot drew up the fixture list himself as it always favoured United.
Ferguson, meanwhile, branded Benitez "lucky" last year for walking into the Chelsea job, saying it would be the second time he had the chance to win a world club title without having to do anything and with a team put together by someone else.
Benitez succeeded Jose Mourinho after Inter Milan's 2010 Champions League triumph but was sacked soon after their Club World Cup victory.
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