I once saw a toddler accidentally knock another toddler over. The caregiver asked to pusher to say, “sorry.” He did. And then helped his buddy up just to push him down again and repeat, “sorry.”
There is way more to an apology than a magic word.
You were wrong. You and your kiddo both knew it. BUT, you apologized. You changed the script. You modeled humility, honesty, and commitment to growth and doing your best. And they forgave you. Nicely done.