Klopp has won the FA Cup, League Cup, PL, CL, World Cup for clubs and the UEFA Super Cup during his time for Liverpool, a feat only previously achieved by SAF. So yes, that's exactly what he was brought in for.
"Only" winning the FA Cup and League Cup after being in the position we are currently in, might indeed feel like a disappointment right after the season but in no way is winning two cups to be considered as a failure. The league was always a long shot, and the CL final is literally a coin toss at this point.