Lloris's first act was to pick the ball out of his net after Mohamed Salah dispatched a second-minute penalty, Moussa Sissoko having been penalised for handball inside the first minute.
A scrappy contest unfolded thereafter and Spurs' best chances fell to Dele Alli and Lucas Moura shortly before substitute Divock Origi rifled home Liverpool's second three minutes from time.
"It's always painful to lose a match of such importance," Lloris said.
"It's hard to start the game this way but we did not get deflated, we played with our principles.
"We were a little too shy before and woke up in the last 15 minutes. It's a shame.
"We tried to do what we normally do but it was easy to defend for Liverpool."
Harry Kane completed 90 minutes on his first appearance since injuring his ankle during the first leg of Tottenham's quarter-final win over Manchester City in April, but spearheaded an attack that failed to fire.