If your straps do not hold your non-cleated shoe in the clips, it may be your clips are too small.


If the ball of your foot is over the pedal's spindle (as it should be), the tightened strap will be behind the ball of your foot (the widest part of your foot). Cinched down, the strap should hold your foot in the clip because you will not be able to get the big ball of your foot.


Pull the strap behind the knob and then cinch it down.


I ride with clips and straps and my feet do not come out of the clips because of the strap's location.