Alan took on the role of Harry, a managing director of a design agency who is married to Karen but seduced by Mia at work
"We're not doing everyone. We're doing about two thirds of people," Richard continued explaining the lack of tribute for Rickman.
He also revealed that actress Emma Thompson, who played Alan's wife in the feel-good film, will not be making an appearance either.
"Ems isn't in it. She just can't do it."
While Harry wanders into the lustful arms of Mia, he decides to stay with wife Karen at the end of the movie for the sake of their two children.
Rickman, who also starred as Professor Severus Snape in the Harry Potter franchise, tragically passed away in January 2016 from secret battle with cancer.
He left behind his loving wife Rima Horton, who he wed in 2012.
Meanwhile, Liam Neeson was pictured last week filming scenes in London with onscreen stepson Thomas Brodie-Sangster [Sam], who is now 26.
The pair were joined by LA-based actress Olivia Olsen, 24, who was just 11 when she played Sam's childhood love interest in the movie.
Keira Knightley, Colin Firth, Liam Neeson, Bill Nighy, Andrew Lincoln, Martine McCutcheon and Rowan Atkinson will all appear in the 10-minute short, Comic Relief Actually
Red Nose Day Actually will air as a part of BBC One's Red Nose Day coverage on March 24 in the UK and on March 25 in the US on NBC