The pressure recommended by who?
If you're going off the printing on the tire's sidewall, that's the maximum recommended pressure. In other words, the manufacturer doesn't want you to go over that amount because the tire wasn't designed for it. Running under that amount is just fine. Unless you're a heavy rider on very narrow tires, 125psi is overkill.
Anyway, I consider a frame pump to be useful only in emergencies. If it gets the tire to a useable pressure, that's fine. I use a floor pump at home to a proper job of it.