The current world number three breezed bast fellow German Altmaier in straight sets as he booked his place in the second round of the Australian Open.
Despite the impressive victory, there was only one topic dominating the discussion in the post-match press conference - Novak Djokovic.
When asked about his thoughts on the Serb being deported and missing out on the Grand Slam, Zverev said: "It wasn't easy for anybody. I think especially for him [Djokovic].
"He had the visa, then got it taken away once he arrived here, then won in court and was allowed to practise, was allowed to stay in the house. Now he had to go back home to Serbia so it wasn't easy for anyone, but for him especially.
"It's very difficult to say something, it's very difficult to say the right things but in my opinion, Australia has suffered a lot. Australia has been a closed country for almost two years and I understand it from that perspective, I understand the tough rules that we had last year."
The Olympic gold medallist also heaped praise on the CEO of Tennis Australia, Craig Tiley.
The 60-year-old has been in the position since 2013, however the last two Grand Slams in Australia have been fraught with problems.
Zverev added: "I have to say one thing, I think Craig Tiley has lost a few years of his life over the last two years, but is doing an incredible job.
"To make the event happen last year when the country was completely closed and to make it happen this year again is one hell of an effort so I think he deserves a lot of credit."
The 24-year-old also slammed the lack of communication which led to the Novak Djokovic saga.
He said: "I understand the Australian people's perspective, I understand the Australian government perspective, but I also do believe that there should have been more communication between the Victoria government and Australian government before Novak came here.
"Once Novak came here, it was very obvious that all of this would start if the government didn't approve of his visa. It is very difficult for him to be in a position that he is in now, I think the whole world is talking about it, the whole world is talking about one of the greatest tennis players, one of the greatest athletes who ever lived, in such a negative way. Which I find very difficult.
"I think there should have been clarity. I understand the perspective that, if they say 'no unvaccinated players should be in Australia' then he shouldn't have got into the country. That's it. Then all of this drama would not have happened.
"From my perspective, I feel a little bit sorry for him in the way the world speaks about him."
The player was also asked about his thoughts on the news that unvaccinated players will not be allowed to compete at the French Open.
Zverev credited the organisers for making the rules clear right from the start - something he believes should have been done in Australia.
He said: "At least it's clear with what's going to happen. At least they're saying 'no unvaccinated players are allowed to play in the French Open'. We know. We know that now in advance.
"I can imagine there's not going to be any exemptions and that's okay. Every country can decide for themselves. I am a fan of letting everybody decide for themselves, if they want to get vaccinated or not. I think that's a decision you are allowed to take. But I'm sitting here and playing the tournament.
"If they're making it clear from the start - that's fine. I think there's not going to be mistakes that happened here."