The push up is not just an arm & chest exercise...in fact, hardly even. The push up, done correctly, should utilise the gluts; abs; obliques & deep core muscles for trunk stability. It should be a smooth, controlled movement. The inability to perform a good, strong pushup could be a sign of trunk instability.
There are several ways to regress the push up. Firstly, the fitball push up is a great regression of the knee push up if you lack the pelvic stability to perform knee push ups. It works on strengthening your midline in order to be able to progress.
The next progression is the knee push up and then the full push up coupled with plenty of core work to improve stability and strength.