McKinna coached the Mariners in their first five years in the A-League and has since served as Gosford Mayor but Mielekamp said now that McKinna was working for a rival club he should restrict his comments to Jets business.
Central Coast announced on Friday that veteran defender Josh Rose had been released from the final year of his contract with the club. It was subsequently announced Rose had signed a one-year deal with Melbourne City.
McKinna was quoted in a story on FourFourTwo website saying "fans are wanting to know why Josh Rose has gone".
"I'm at the Jets now, I'm just focusing on what's happening here, but Josh Rose has been a great servant," McKinna said.
"Josh has got his reasons for leaving. I sent him a message just so I can wish him all the best and he got back to me.
"If that was Newcastle Jets, I'd be letting people know why people like Josh Rose have left the club. I wouldn't be having speculation there because there is too much speculation at the moment."
But Mielekamp stressed Central Coast had included a detailed message from Rose in the club's media release announcing the player's departure, in which Rose, 34, said he didn't want to stand in the way of young players coming through at the club.
"I probably haven't had the best 12 months, football-wise, for myself, but things in football can change pretty quick and at the end of the day this is the best decision for myself and the club," Rose said.
"The last thing I want to do as an experienced senior player is limit the playing time of any junior and young Mickey Neill has come along in leaps and bounds and is really making that left-back spot his own.
"That was a big part of my decision and I see that as his position now so hopefully me moving on will help him realise that even more."
Mielekamp told The World Game he had spoken to McKinna to voice his concerns.
"We gave Josh the opportunity to have a one-on-one with our members to explain and he did a really good job in explaining his decision," Mielekamp said.
"Lawrie needs to focus on Newcastle. I'm sure everyone in Newcastle wants to talk about Newcastle, not the Central Coast Mariners.
"We gave Josh Rose every opportunity to speak openly and honestly and there isn't any more to it. I think Lawrie is speaking without all of the information available to him.
"I've spoken to Lawrie to clear the air. Lawrie has assured me it was never his intention to come across this way in the article and I made the point to him that we made sure Josh Rose had a personal message to our members in his own words."
McKinna was also quoted on the Central Coast coaching situation in the article, suggesting the club should go for an Australian coach to replace Tony Walmsley, who was sacked earlier this week.
Mielekamp said the Mariners would fill the vacant coaching spot how the club saw fit.
"It's not Lawrie's or any other CEO's place to make comments about opposition coaches or players," he said.
"It's totally inappropriate. We would never make comments about the coaching situation at another club, nor expect any other club to make comment about our coaching position.
"I'm sure Lawrie would hate for me to talk about his coach or players in any way. He understood my concerns, when I spoke to him."
McKinna told The World Game it was never his intention to come across as if he was questioning the actions of his former club.
"If anybody took my comments the wrong way, I apologise for it," he said. "I was just making the point Jose Rose has been a great servant for the Mariners and he'll be sadly missed by the fans."
Mielekamp said Rose had made the first move about leaving.
"To be honest, he approached us and in his own words he talks about Mickey Neill in that fullback spot and the reality was Tony Walmsley was playing Josh more as a centre-back, which isn't his natural role," Mielekamp said.
"Josh came to us and said he was looking at an opportunity at another club where he could play in his favoured position and he is a club legend, so for us we have all the respect to do the right thing by Josh.
"What it does create is the opportunity for us to now recruit a strong centre-back, so at the moment it's a situation where we're saddened to see him move on, but he said himself he's doing it in the best interests of the club."
The Jets-Mariners trial match kicks off at Scully Park, Tamworth, at 4pm.