I think some experiences in education are definitely helpful, but experience is not the only criterion the admission committee looks at. I am now in the human dev program in master's degree in HGSE, but I am from counseling background rather than teaching. Some of my classmates do not have any experiences in full-time teaching or related positions, they just graduated from college!
I asked one of the faculties who also served in the admissions committee, he said that the most important criterion is whether your interests meet the specialties of current faculties, which should be shown in your SOP. It is totally fine if you do not have a very particular interest to pursue, since master's degree is a time for students to explore a larger possibility in any educational fields.
I am sure GRE is not an indicator of the admission, since I got a silly score on it: 470 Verbal/740 Quantitative/ 4.5 AWA (lol). Though I am an international student and my native language is not English, still the score is so funny. My college GPA is 3.96, much better than the poor GRE. Aside from GRE, I have worked in a public middle school as part-time school counselor intern for a year, full-time military counselor also a year, and that's all. I did one research in college and it was full-granted by the government. Some experiences in leadership in student society and orchestra might help my application. I know I got strong LORs, though none of my recommender is HGSE alumni.
I am sorry to hear that you were rejected. however, in my opinion, if you plan to try again, tailor your SOP to meet your interest and the faculties specialties might help. Good luck!
