Understand that the phrase uses the process of cooking as a metaphor for achieving results. Implementing the new policy was tough, but you can't make an omelette without breaking eggs.
Pro Tip 2/3
Expect Sacrifices
The phrase implies that sacrifices are often necessary to make progress. We lost some hours of sleep during the project, but you can't make an omelette without breaking eggs.
Pro Tip 3/3
Change and Consequence
Use when discussing the unavoidable negative side effects of change. The new highway displaced some wildlife, but you can't make an omelette without breaking eggs.