Just as you would with ANY meal from ANY nation, you would eat Indian food with a fork and knife. You may occasionally require an additional spoon.
The fork is used to a. hold the food while cutting and b. transfer it to the mouth. The knife is used to cut portions.
Eating Indian food with a knife and fork is extremely simple, though it does take some practice:
To cut a slice off of food like roti or dosa, poke a fork into it and move the knife across it. Before biting into the piece, dip it into the chutney, sauce, or whatever.
When consuming rice-based foods or those that resemble them, use the knife to push the (mixed) rice onto the fork and then bring it to your lips. If you hold the fork horizontally, the contents will fall off! Wet material is best placed on the concave side of the fork, whereas dry material is easier to put on the convex side of the fork tangs.
Refrain from feeling ashamed. Before I travelled overseas for the first time, a long time ago, I got comfortable with chopsticks, knives, and forks when eating Indian food.