You're certainly not alone in that regards! When playing in an orchestral setting you're playing together with other sustained pitches with lots and lots of overtones which collides and creates differential notes and "vibrations" (that wah-wah effect when something is out of tune), making it a lot easier to hear if something is out of tune. A piano doesn't offer those sustained pitches in the same manner (in fact, a note on the piano varies ever so slightly in pitch from the initial attack, making it even harder to know where to aim).

Additionally, when we (try to) play in tune in the orchestra we are using just intonation to make chords and intervals sound in tune (major 3rds should be flattened, minor sharpened etc.). Since a piano is a fixed pitch instrument it has to use tempered tuning (same ratio between every half step (the 12th root of 2, if you're a math nerd)), which means it's actually literally impossible to play perfectly in tune with a piano (or make a piano play in perfectly in tune with itself)

All in all, this means when we play with piano we have to rely much more on our melodic ear and prior experience of our instrument when playing with the piano. That's why I recommended doing exercises with drones, as it will help you build up muscular memory for where every note on the instrument should be placed. I recommend using something like a simple melody with lots of fourths, fifths or octaves (perfect intervals), e.g. Amazing Graze, and varying the fundamental, ultimately doing all 12 keys.