Zingarevich took over as the owner at the Madejski Stadium in January and has since seen the club return to the Premier League.
Despite struggling in the initial couple of months of the season the Russian offered his support to McDermott ahead of last weekend's victory over Everton, amid speculation he was lining up a big name replacement.
Although McDermott said he did not need to hear the comments publicly from Zingarevich he did thank the club's owner for clarifying his position.
"I get on really well with Anton and I know him well enough, he didn't need to come out and say anything, that was up to him to say whatever he had to say," he said.
"I've known him since January and we have been very consistent with each other and have a good relationship.
"It wasn't particularly important to me and I don't think it was particularly important for him to say it - but I appreciate the fact he did say it."
The 51-year-old was given the backing of his owner only days before Chelsea's Roman Abramovich sacked Roberto Di Matteo just six months after he delivered the Champions League to Stamford Bridge, but McDermott believes a club's owner has the right to do as he sees fit.
"It is what it is in football, you've seen what happened yesterday, you know the business we are in, I've been in it for 34 years," he said.
"The owners are the owners, they are entitled to do whatever they feel is the right thing for their clubs.
"The Chelsea owner has done what he did yesterday and it is what it is, you can't affect what the owners do at any given club so you just have to do the best you possibly can on any given day."
The 2-1 win over Everton, the Royals' fist league success of the season, would have helped relieve any remaining pressure on McDermott and has confirmed his belief in his players.
He said: "They (the players) have been competing at this level and have been getting draws but now they have turned those draws into a victory - we've got the first victory, we don't have to sit here talking about the fact we haven't got that victory and now we can move on and look forward.
"They played against a top side, Everton are a top side there are not doubts about that, so it is a really good win for us. It was a great win for us, we needed that."
A Steven Naismith goal had seen Everton go in at half-time in front but Reading emerged for the second 45 minutes much more hungry for the ball and a brace from Adam Le Fondre secured a memorable win for the Berkshire club.
McDermott played down his half-time team talk and reckons his players should take confidence from their second-half display into their match at Wigan on Saturday.
He said: "They weren't stern words (at half-time), I was just trying to guide them in the right direction - that we had to have a belief and step up and play the Reading way, and I think we did that.
"We rode our luck and it was probably the first time this season that we have had a bit of luck. We need to play the way we play, if we can do that and compete with the likes of Everton then we can compete in this league.
"The performance of the second half is the momentum (for Saturday), that is what we want to keep going, that belief to keep playing our game, keep the ball and do what we have to do.
"Everyone is in a good place, we won a load of games the back end of last season and the place was as good as it was last week.
"So we are just going about our business and doing what we have to do."
McDermott has welcomed goalkeeper Alex McCarthy and midfielders Jimmy Kebe and Jem Karacan back to training this week, with Danny Guthrie to return over the weekend as he looks to get a full complement of players fit and ready for a busy December which sees 17th-placed Reading contest seven league games.