。
Don't laugh at my failure.
Literal
I [of-の] failure [object-を] don't-laugh [give-くれ].
笑う ('to laugh') takes を for the object being laughed at — 'laugh X' means 'laugh AT X' in Japanese. No preposition needed, unlike English. The 僕の失敗を ('at my failure') + 笑わないでくれ ('don't laugh, for me') is a direct emotional plea.