The Chelsea interim manager had said Sir Alex ignored him ahead of the FA Cup sixth-round clash between the sides at Old Trafford.
Benitez also suggested that reporters ask the Manchester United boss for his take on events if they were "brave enough".
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"Why wouldn't I shake hands? Think about it. Have you ever seen me not shake hands with anyone?
"I never saw him [Benitez]. I was signing autographs at the front. There's that Indian lad who always wants to shake my hand before the game, and says it brings me luck.
"I was signing autographs and I moved across the stairway to where they all gang up to get autographs, so I never saw him.
"Why he would say that, I've no idea. If he wanted to shake my hand he could have walked straight in front of me.
"I don't know why he's said that, I've no idea."
Sir Alex also confirmed both Nani and Phil Jones will miss Saturday's clash with Reading, who sacked Brian McDermott on Monday.
"Nani came off against Chelsea but it is not serious and it will only be a couple of weeks out," he added.
"We thought it was another bad hamstring injury but it’s only a slight one. Hopefully he’ll be ready for action after the Sunderland game.
"Phil Jones is not back yet, but he should start training next week. The players have done well in training this week and hopefully we’ll be OK [Saturday]."The United manager also had his say on the Royals' decision to relieve McDermott of his duties.
"Reading are fighting for their lives at the bottom and could come here without a manager," he continued.
"Some things you can never understand. To sack Brian McDermott at this stage of the season is strange to say the least."