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Robertson pointed to the spot - allowing County to tie the game - after Alex Schalk dived in the box, with no contact from the Danish defender.
Rodgers revealed the Scottish FA's head of refereeing, John Fleming, called him this week to discuss the incident.
"I really respected that - he didn't have to," the Celtic boss said.
"Don Robertson doesn't have to ring me or apologise to me, John Fleming did that.
"All I would say to Don Robertson is make sure you apologise to Erik Sviatchenko, because it wasn't a penalty. But I'm sure he will learn from it - we've seen enough poor decisions in the Champions League over the last week or so.
"We have to help referees and help them become better because mistakes happen, but in circumstances like that you have to get them right or you lose the trust of the players."
Schalk accepted a two-match suspension for simulation, while Robertson will be one of the officials behind the goal for Celtic's Scottish Cup semi-final against Rangers on Sunday.
Rodgers, who labelled the penalty award a "horrendous" decision, has no issue with his involvement.
"Do I think he should be involved in Sunday's game? Listen, we will all make mistakes but he needs to get back out on the field and as long as he doesn't make the same one as he did in the match against Ross County, then I'll be happy enough," Rodgers said.
"You have to respect that you don't have the facilities up here that they have in other countries, in particular down south. They're not full-time. The guys up here, I think they're doing their very, very best to educate referees, put them out there in order to perform. So you probably don't have a massive pool of referees that you can put into a game such as this here.
"Don's qualified into the Uefa panel now, so he's going to make mistakes, you always hope they're never costly, but he's got to go again. And if he's involved this weekend, then good for him."
Brendan Rodgers says referee Don Robertson should apologise to Erik Sviatchenko for awarding a penalty that cost Celtic victory over Ross County.