The goalkeeper was in the starting XI as one of 10 changes made by head coach Andoni Iraola for the third-round tie at Anfield.
It was Mamardashvili's first appearance of the season and he played a key role in helping the Reds progress through in the tournament with a number of fine saves.
At the other end, goals from Alexis Mac Allister, Cody Gakpo and Dominik Szoboszlai clinched Liverpool a 3-1 win.
"[It was] crazy, we lived everything, the weather as well! But a good game. I enjoyed it," Marmardashvili told Liverpoolfc.com post-match.
"I'm happy to have made the saves because I helped the team a little bit. Yeah, happy."
The Georgia international produced a crucial stop when he halted a deflected shot from Spurs forward Omar Marmoush with the lead at 2-1 late in the second half.
On the importance of that save in particular, Mamardashvili added: "This one, I saw [back] just now. It was really crazy. A good save.
"It was a really important game, a really important victory. Especially at Anfield with our fans. Really happy.
"I hadn't had any opportunity to play this season, so I wanted to enjoy today and I did. Let's see what happens next."
Read Andoni Iraola's post-match press conference