World No. 3 Zverev's hopes of a first Grand Slam title were dashed by Novak Djokovic in the quarter-finals of Roland Garros, the Serbian defeating the German 4-6, 6-3, 6-2, 6-4 last week.
It was the first time since 2020 that Zverev had failed to reach at least the semi-final of the event, and extended his wait for an elusive major.
The 28-year-old's career was put under the microscope on German TV following his defeat, with tennis icon Becker, a six-time Grand Slam winner, and Billie Jean King Cup captain Rittner among those sharing their thoughts.
Becker and Rittner were critical of Zverev's approach to the match, but a large focus was on the German's coaching situation.
Both former pros suggested that he needed to move away from his father, Alexander Sr, and brother Mischa.
"At some point, you need new noises and a new environment. It's the same in football, as a football coach you don't normally stay with a club for 10 years," commented Becker.
"He [Zverev] is the one who decides. He is the chairman of the board, the CEO. He decides what Team Zverev will look like in the future. His father and brother did an excellent job, but it wasn't good enough for the final step."
Following a short break, the world No 3 returns to action at the Stuttgart Open this week, looking to ramp up his grass-court preparations ahead of Wimbledon.
And, asked about both Becker and Rittner's comments, the three-time major finalist was quick to counter their claims.
"When things are going well for me, I always do everything right," said Zverev.
"When things are going badly for me, everyone else is very, very clever. Unfortunately, Boris is one of them, and so is Barbara Rittner.
"I don't know why she [Rittner] suddenly has so much to say about my tennis career. To be honest, I don't take her opinion seriously. Firstly, because of that, and secondly, because I think she's wrong.
"I lost to Djokovic. Maybe it wasn't my best match, but I thought he played very well - it was just difficult.
"And to be honest, I talked to Boris a lot, had a lot of contact with him before he made those statements. Before this crew had all that to say, I had a great relationship with him. I don't know why it all has to be like this now."
Zverev was speaking ahead of his opening match in Stuttgart, with the German set to face mercurial Frenchman Corentin Moutet on Thursday.
And, despite disagreeing with Becker's comments, he insisted that he would always be willing to talk to the world No. 1 to discuss their issues.
He added: "I will always talk to him [Becker] if he wants to talk to me.
"In every relationship, whether it's with a partner or someone else, there are issues to argue about. This is perhaps one of ours at the moment.
"I still have enormous respect for him. He is an absolute legend, not only in sport, but in Germany in general, and also worldwide. I will always listen to what he has to say.
"But I don't always have to agree with him."