Is it loose? Does it rattle when you shake the gun?
Did you follow the owners' manual's directions completely and to the letter?
When you put the slide back onto the frame, did you make sure that the grooves in the slide mated properly with the frame?
Did it not exhibit this "give" before you shot and cleaned it?
When you write "push the slide down," do you mean vertically down, from the top toward the trigger and the grip? Or do you mean from front to back? (This is important.)
How 'bout when you pull the slide upwards?
Did you clean the pistol thoroughly before you first shot it? Or only afterward?
Semi-auto pistols can't be too tightly assembled, or they will not operate properly. (There are exceptions, but not in your case.)
Some vertical play in the slide-to-frame fit is good. A lot of free play is bad. If there's a lot of play, you have reassembled the pistol incorrectly.
If there is front-to-back play, you have reassembled it really, really badly. It might be dangerous to you.
Manufacturers ship out their pistols coated with some sticky anti-rust compound, which should be cleaned off before the first shot is fired. The sticky compound might've made the slide a tighter fit on the frame than it really is supposed to be. Now, cleaned, the slide may seem to fit loosely.
An easy fix: Take it apart again. Now, reassemble it in very strict accordance with the owners' manual's instructions. Check for missing or broken parts as you go along.