What you did is called "rinsing," not "washing." "Washing" involves treating the yeast with acid to kill off bacteria in a contaminated culture. This also significantly weakens the yeast, so if you think you need to do this, it's best to just buy new yeast.
Rinsing with water is detrimental for several reasons. It raises the pH by replacing beer with water, leaving the culture susceptible to bacterial infection. Osmosis causes the yeast to expel minerals, aminos and other nutrients needed for healthy yeast. It adds oxygen, causing the yeast to immediately begin respiration and metabolism, but without new food they just consume their reserves, becoming weakened; therefore it should not even be done shortly before pitching.
Best practice is indeed to store the yeast under the beer it fermented -- just pour the slurry from your fermenter into a sanitized container and save for reuse. Efforts should be made to exclude oxygen from the beer to prevent the above mentioned premature metabolic processes, and to avoid providing oxygen to acetic acid bacteria which are inevitably present and could feed on the alcohol present.
When repitching, pour off enough of the beer so you can swirl and shake the yeast up into a thick slurry, and pitch directly into the wort. There will of course be some non-yeast material in the slurry -- trub and non-viable cells. Standard practice is simply to pitch a larger amount of slurry to account for this.
The practice of yeast rinsing came into homebrewing some time ago the same way so many bad practices have, by the serial repetition of information from books that were half a century or more out of date.