The German felt ill on Friday night, with club doctor Andy Massey diagnosing the problem on Saturday and the manager was taken to Aintree Hospital.
He had surgery at around 1:30pm and was informed of his side’s result following the procedure.
Klopp’s duties were overseen by his backroom team, including assistants Zeljko Buvac and Peter Krawietz, first-team development coach Pepijn Lijnders and goalkeeping coach John Achterberg.
Liverpool had been 2-0 up at Anfield, but conceded twice late on to drop points as supporters staged a walkout protest over ticket prices on 77 minutes.
The Merseysiders have an FA Cup fourth round replay at West Ham on Tuesday, but it is unclear at the moment if Klopp will be back in the dugout by then.