In this video

Take a specialized carpet repair needle, a very fine crochet hook, or a similar thin, pointed tool. Insert the tip of the tool into the carpet pile adjacent to the pulled loop. Carefully hook or push the pulled fiber back down into the carpet, guiding it through the existing loops to mimic the original carpet texture. This action may need to be repeated multiple times, working the loop back in small sections. Around the 0:12 mark, if any tiny frayed ends appear, they can be carefully snipped with fine-tipped scissors or tweezers to maintain neatness.