The midfielder, now 29, left Bayern in 2018 in a deal worth a reported €16 million (£14/$18m), signing a four-year contract.
But his first season with Schalke did not live up to expectations.
Rudy struggled and so did his club, managing just 33 points and finishing the season just five points clear of the bottom three, a far cry from their second-place finish in 2017-18.
With the Bundesliga campaign having now drawn to a close, Rudy has vowed to prove his critics wrong with a stronger showing next season.
"I did not show what I can do," he told Goal and SPOX. "That's why I'm disappointed with my personal performances.
"From now on, I will take things a little differently and try to show what makes me strong. I want to prove to my critics wrong, I can do it better - this thought motivates me immensely."
The midfielder says the transition from Bayern to Schalke was more difficult than expected, but that his high standard for himself were not met.
"I underestimated the differences between the clubs. It took me a long time to get used to the Schalke game, which made my time at the start very difficult. That will certainly not happen to me again.
"I also have high expectations of myself and try to get the most out of every game and every training session.
"I would not say that my expectations were too high. Fans and clubs rightly expect a lot from me and can expect a lot in the future as well. I know what I can bring to the team and I will show it next season."
While Rudy vows to be better next season, he admitted that the constant criticism thrown his way have had a negative impact on him.
"It's not nice to be constantly criticised," he said. "Of course, legitimate and constructive criticism is part of the job and is also important, but I do not understand why only negative reports are made about individual players.
"That does not go by without a trace and it hurts. People have to realise what they're causing. Football professionals are not machines, but people with feelings. Sometimes you get the impression that you just get blown away."