Make sure you can measure cadence (your pedal RPM). As others have said find your rhythm using your gearing and maintain a more constant cadence.
I ride but not hardcore but have recently started using a smart trainer which mimics hills. Just like being outside I'm try to maintain a good cadence at all times even hills. If you find your bike doesn't have a low enough gear (you seem to strain in the lowest gear) you should look at having a different cassette fitted that has a lower gear like Joey mentioned. Most recent bikes have long cage derailleurs that allow a larger diameter cassette (lower gearing) without other changes but your local bike shop be able to help.
Let us know what gearing your have and type of bike (number of gears on crank and rear wheel)