Ferguson accused him of stirring up trouble after the recent FA Cup tie at Old Trafford.
"I never even saw him at Old Trafford, so I don't know why he went and made such an issue of it (the handshake)," he said.
"When we went down to Stamford Bridge we shook hands before and after the game. There are no problems for me. We do it all the time. It is part of the English culture that you do that.
"At the end of the game, we always shake hands and always have a meeting in my office with both sets of staff. It is a fantastic thing to do. You don't get it abroad, but it is the right thing to do.
"It is an opportunity to get away from the game itself. You maybe see managers twice a year, when you play them, so that opportunity to spend half an hour with them after a match is vital. You can discuss your jobs and lots of issues."