An example of the difficulty of translation: "Now get off my lawn". How would you translate this?
I disagree with the translation as it's too literal and totally misses the mark. Your suggestion - 我觉得自己老了 - is better but as you've said, it lacks the tone and nuance of the expression.

Variations on the phrase "get off my lawn" were once uttered by ageing homeowners at disrespectful youths but has long since morphed into a caricature of generation gaps. The original users of the phrase are unaware of generational differences and think it's the kids that are acting badly, whereas the phrase is used in the opposite sense nowadays - its users are keenly aware of generational differences, of differences in experience and perspective, and are using it to point out this fact. You might replace it with "you (younger people) don't understand", "times have changed", and in certain situations, "you should be grateful" and more. The humour in the phrase is that it simultaneously evokes an image of a cantankerous elder futilely railing against inevitable change.

I think there's no way to 100% capture such a meaning and nuance. If I had to offer a translation, I might try 孩子们一边玩去吧 (you kids run along now), but this lacks the humour in the English phrase.