Lots & lots of potential reasons why you are slower on the trainer:

1 - what trainer do you use & how tight is the tire on the trainer? You can get crazy speed readings, especially high ones, if you have the tire on loose.

2 - most, though not all, trainers have small flywheels which equate with low interial load. It means your muscles have to work in a totally different way than they do outdoors on the open road. For instance, try coasting indoors and see what happens to your speed - it plummets, whereas outdoors in the flats, coasting for a few seconds doesn't slow you down nearly as much. Most people find it more challenging on the trainer. So it may take you a while to duplicate your outdoor pace, indoors.

3 - another biggie: cooling/ventilation. heat affects blood flow, which can affect the amount of work your muscles can do. In short, you need to have a lot of air moving in your training space to keep yourself from overheating. You can adapt to warmer training conditions, to a point, but it behooves you to have as big a fan as possible or use a non-heated room or garage.

4 - motivation! no open road, blue skies, green hills, or even another rider in the distance to keep you motivated. Occupying the brain is as big a challenge for most people on long trainer rides as the physical part of the ride itself - so music, videos, etc are very useful.

Good luck with your trainer, I find mine invaluable :-)