Benitez claimed he was waiting to shake hands with the Manchester United boss but Ferguson walked past him without doing so.
The Chelsea interim manager said: "I was waiting at the beginning. It's up to him, I was in the way waiting."
Asked why Ferguson might have done so, Benitez added: "Ask him - if you are brave enough ask him. It was his decision. I was ready and waiting. I have some education because I know a lot of people are watching so I know what I have to do."
Benitez did not attempt to shake Ferguson's hand after the conclusion of the match, which saw his side come from 2-0 down to draw 2-2.
The Spaniard explained his action by saying: "I was with my players celebrating."
Ferguson has admitted Manchester United are lucky to still be in the FA Cup.
United swept into an early two-goal lead against Chelsea at Stamford Bridge today, only to crumble after the interval.
Eden Hazard and Ramires pulled the visitors level and only a crucial late save from David de Gea kept United in the competition, even if they now face a trip to Stamford Bridge if they are to book a semi-final meeting with Manchester City at Wembley next month.
"We are lucky to still be in the FA Cup," said Ferguson.
"We ran out of legs. Our two full-backs, Rafael and Patrice Evra, were knackered and the two centre midfield players tired badly and we kept giving the ball away.
"I detected there were some signs of tiredness. You have to understand the problem is the emotion and intensity of Tuesday night had taken its toll on one or two of the players.
"Understandably I have no problems with that part but it made it a long day for us and they were by far the better team in the second half."
Typically given how much the focus had been on him, Wayne Rooney followed Javier Hernandez's early effort by curling home a free-kick which Petr Cech had expected to be cleared.
At that point United seemed to be cruising. But a couple of missed opportunities gave the visitors' hope and Chelsea looked more likely winners at the end.
"We could have been four up in the first 25 minutes," said Ferguson.
"Wayne and Javier's goalscoring has been great this season.
"We needed that because by the end of the first half I detected our legs were starting to go.
"It was a very good save by David de Gea near the end. If they had scored then we were out there would have been no doubt about that."
No date has been set for the replay, although should Chelsea progress in the Europa League this week, it will inevitably mean the Londoners either facing four games in an eight or nine day period, or the postponement of Premier League games, one of which could be the Manchester derby.
The Football Association are expected to offer an update tomorrow, although Ferguson will be more concerned about Nani, who limped off with a hamstring injury just before the break.
"I don't think it is serious but he had to come off," said Ferguson. "It was unfortunate because he was playing well."
United defender Rio Ferdinand could be in hot water with the Football Association after an off-the-ball altercation with Fernando Torres.
Asked if he had seen the incident, Benitez added: "I haven't. Fernando mentioned it - but you can see the replay."
Benitez insisted that Chelsea deserved to win having come from two goals down and having been denied victory by the David de Gea save from Juan Mata right at the death.
He added: "We analysed the game and we deserved to win. The first half we made two mistakes and conceded two goals but in the second half we were on top of them and had a lot of chances so it was a good game."
The Chelsea boss also insisted United had had everything in their favour.
Asked if United had suffered from tiredness after their Champions League defeat by Real Madrid last week, he said: "I thought you were joking, they play on Tuesday, we play in Romania on Thursday.
"They had everything in their favour, they are playing at home, they played on Tuesday, we are coming from Romania and had to travel again so we did a great game and I'm really pleased with my players."
Benitez admitted bringing on Eden Hazard and John Obi Mikel had changed the match in Chelsea's favour - Hazard responded almost immediately with a brilliant goal.
He said: "We knew that we had to change something and we knew Hazard is a player with quality who can make a difference and he had fresh legs as well.
"I asked Frank to give 100 per cent until then and he did. You have to manage the squad.
"We saw the character and the reaction that I was expecting so until the end of the season we will be fighting."
The winners of the replay will face Manchester City in the semi-finals but such is the fixture pile-up that there is no obvious date for that replay to take place.
Benitez said: "I cannot say when I prefer, we have so many games it depends on the dates. It is an FA decision."United defender Rio Ferdinand admitted the team had been punished for being careless.
Ferdinand told MUTV: "We gave them the impetus to claw their way back into the game. We played some great football at times but were so careless at times. If you are careless you are going to get punished. That was the case.
"There wasn't a mental reaction to Tuesday but maybe physically you could see it in a few of the guys' legs, and as the game stretched and became a bit more open there were some tired legs out there.
"But that is no excuse. We should have had the game sewn up before then and with the experience out on the pitch we didn't utilise it the way we should have.
"But we are still in the cup. Wembley is waiting for one of us to go through and hopefully it is us.
"We go to Stamford Bridge for the replay with confidence. We have the tools. We have been there before this season and done well, and with the squad we have we don't fear going anywhere."