The panel was also attended by Robinson's 90-year-old widow, Rachel; plus Harrison Ford, who plays Branch Rickey; Chadwick Boseman, who plays Jackie; and the film's director, Brian Helgeland.
Michelle Obama said she and President Obama watched the movie over the weekend while their daughters, Sasha and Malia, were away, and would make sure the girls watched it.
"We think that everybody in this country needs to watch this movie," Michelle Obama said. "And I can say with all sincerity that it was truly powerful for us. I don't know about you, but we walked away from that just visibly, physically moved by the experience of the movie, of the story.
"Watching anyone go through what Jackie and Rachel Robinson did -- the outright discrimination they encountered at every turn, from the fans in the stadium to the airport receptionist, even from some of his own teammates -- and you're left just asking yourselves, 'How on earth did they live through that? How did they do it? How did they endure the taunts and the bigotry for all of that time?'"
The first lady added that "42," which opens in theaters April 12, offers powerful lessons not only in personal courage but also in the benefits of hard work and dedication.
"It would have been easy for them to get mad, because I know I was mad just watching the movie," Obama said. "It would have been easy for them to get mad or to give up. But instead they met hatred with decency. And, more importantly, they gave their absolute very best every single day.
"And I can't say this enough to young people: You might not be able to hit a ball like Jackie Robinson, but you can get your education. In fact, you must get your education and demand more of yourself every single day. You have to do that, and you have to pick up yourself when somebody knocks you down. Because you will get knocked down. But to do all of that, you have to put the work in."
Obama said she was truly honored to be in the presence of Rachel Robinson.
"She's a woman of strength, of courage, conviction; a woman who paved the way for me … paved the way for millions of Americans all across this country," the first lady said.
"Her presence here today makes us realize just how connected we are to that part of our history. It is very real and very tangible. In the end, I can't help but marvel at just how far we've come over the course of this woman's life. But it also reminds us how far we have to go, how much more work we have to do."