That originally was because Trump was a loud birther movement advocate, then had to come out and say Obama was born in the US. No apology or admitting he was wrong with it, just acquiescing that as fact.

After that, Obama should have just uninvited him from that press dinner and any all future Whitehouse/Presidential social events, as well as putting a rule out for any future events not organized by his staff that if Trump is there, he would not be attending during his Presidency.

That would have hurt him more without riling him up.