I'm always sceptical of these narratives about managers being serial bottlers, I remember the same things being said about Ferguson and Klopp when they missed a few things they could win.
Some people now day the same thing about Pep and the champions league.
The fact is margins are very tight and most managers even the very good ones miss more than they win and they cannot control every error on the pitch.
Rodgers produced a good team at Swansea who neither bottled promotion or were threatened with relegation.
His team at Liverpool were very good with Suarez and just missed out. He won plenty at Celtic and they weren't bad in Europe.
Leicester won a very good FA cup and have over achieved in the premier league.
He is undoubtedly a good coach and I seriously doubt he is a bottler.
All that said I don't want him as our manager, I find him unbelievably narcissistic. His favourite picture is a mirror, and all the Celtic fans I know thought he was a liar when he was at the club and can't stand him since he left.