Absolutely - the pedals are probably most of the problem... You've been using clipless on the spin bike and have become accustomed to being able to pull up. When you switch to the platforms on your road bike you're probably still trying to do that. The few times I've been on a non-clipped bike recently I've had a hard time not lifting my feet off the pedals - especially when it is taking some effort and uphills when I am used to being able to pull up.

You can put the toe clips back on and leave the straps off, but honestly I think toe clips are harder to learn to use than dual sided clipless models, especially if you been doing it on the spin bike and know what it feels like to clip in and out. Yes, there is the danger of forgetting to clip out and falling over, but with toe clips so many beginners have to look down trying to flip the things over and you can still forget to take your foot out.