Palace were hoping to wrap up a season-long loan move for the Arsenal midfielder when he became available in the final week of the summer transfer window.
The Eagles held talks with the player, but much to the frustration of the club, he opted to join Bournemouth instead and is doing well at the Vitality Stadium.
However Parish says he does not beat himself up over the fact they missed out.
"I know we didn't get Jack Wilshere, but that was right in the last week of the transfer window and suddenly he is available on loan," said Parish.
"People think that sometimes you are procrastinating, but it's not and you know that things will come up. The jigsaw pieces don't fall into place for everybody until sometimes the last couple of weeks.
"One player moves and that frees another player up, someone like Jack becomes available because maybe he won't get the minutes and he wants to go out on loan, and you have got a little bit left in the tank.
"Obviously he is doing great for Bournemouth and we might have made that happen, you never know, but I don't like to be too down about it, because you don't know what opportunities will present themselves."