Roland Lamah's late effort was controversially ruled out for offside at West Brom by Betts at the weekend.
Laudrup claimed "when you make a big mistake, there should be consequences" after replays showed Baggies players Ben Foster and Gareth McAuley touched the ball before it rebounded to Lamah.
But Betts raised his flag and the decision doomed the Swans to a 2-1 defeat and meant they were leapfrogged by their opponents into seventh spot in the Barclays Premier League.
When asked if Betts should have a spell out of action, Laudrup said: "I think in life - and in football as well - when you make mistakes there are always consequences.
"If one of my players crosses the line and kicks someone, he gets a red card and up to three games on the bench.
"So when you make a big mistake, there should be consequences.
"In Spain, when somebody makes a very big mistake, he goes into what they call the 'freezer' - meaning they go out (from officiating) for some weeks, like a red card.
"But that won't help me personally or my team because we won't get those points back.
"It's not life and death for us, this game, but it is just frustrating that things like this happen."
Laudrup believes Betts should apologise to Lamah and own up to what he believes was a blatant error.
He said: "No-one has to apologise to me, but he (Betts) should apologise to the player.
"I'm really looking forward to seeing what the comment was (on why the goal was not given).
"Of course it always helps if someone admits they've made a mistake, instead of trying to justify it."
Laudrup admits he is already making plans for next season, when Swansea will be competing in the Europa League after their Capital One Cup triumph.
He said: "Right through January, I was asked about which players might be coming or going, like every other manager.
"But just because February 1 came around didn't mean we could be relieved and stop working because it never stops. We are already working for next season, right through the last month.
"The Europa League doesn't mean we'll have a larger squad. I don't believe in too big a squad. Of course there will come some new players, in strengthening certain positions.
"But I don't think it's the moment to talk about the names, who's coming, who's leaving, because we have nine games to go.
"The most important players are those who are working here now. But of course, backstage we still work because we can't wait until May 20 (the end of the season).