You are possibly using the wrong size wirenut for the number and size of wires you are connecting, or simply installing them incorrectly.

"Saving money" is a dubious justification for tackling electrical work if you are not up to the task - the money you "save" can easily cost you a good deal more when your work fails in a more dramatic fashion and burns the house down or injures/kills someone.

There are "push-in" wire connector blocks made and listed now. I'm not personally a fan of them, but they are made and listed.

i.e. this image from ideal industres (not endorsing or associated, just using the image:)
[![push-in wire connectors][1]][1]


  [1]: https://i.sstatic.net/xasR3.jpg