After Lucas Moura cancelled out Roberto Firmino's first-half opener with just 20 minutes remaining, the Reds were left facing a frustrating result that would see them lose ground to Manchester City in the Premier League title race.
However, the home supporters inside Anfield quickly brushed aside their disappointment and were rewarded with Toby Alderweireld's 90th-minute own goal that put Liverpool back on top of the table.
"For me, when we scored [to make it] 2-1, it was relief as well. It was not like bouncing around and stuff like that," Klopp told Liverpoolfc.com. "It was relief.
"I think first half, of course, we deserved it.