The German world number 189 caused a minor upset on Wednesday as he saw off the former champion in four sets.
"It's going to take a while to sink in," the qualifier is quoted as saying by Sky Sports News. "I'm not normally the type of guy to cry, I don't know what happened. I'm playing Lleyton Hewitt, a guy you're watching when you're growing up.
"I've won a lot of matches already playing qualifiers and a very good first round and that really helped me with my confidence to go into the match believing I could do it."
Brown will meet French world number 111 Adrian Mannarino in round three.