This accident happened because I wasn't looking and just ran straight into the road
This accident happened（ この事故は起こった） because I wasn't looking and just ran straight into the road. （ 見ないで一方的に道に進んだからです）
straight into the road は一方的に 道路に進むって意味です
It was completely my fault because I stepped out onto the street when I shouldn't have. That's why it happened.
この場合、次のような言い方ができますよ。
ーIt was completely my fault because I stepped out onto the street when I shouldn't have. That's why it happened.
「（飛び出してはいけないのに）私が道路に飛び出したので完全に私のせいで起こりました」
completely my fault で「完全に私のせい・落ち度」
to step out onto the street で「道路に飛び出す」
ご参考まで！
オーストラリア 
カナダ 
