The midfielder followed up his spectacular strike against FC Porto with the Reds' third at Anfield on Saturday afternoon.
Diogo Jota scored twice to put the hosts 2-0 up after 32 minutes, before Thiago's deflected strike gave them a three-goal advantage at half-time.
Virgil van Dijk volleyed in the fourth early in the second half as Jürgen Klopp's men sealed their third consecutive victory and clean sheet.
"As I said, it's special to score at this stadium but I am even more pleased with the win," Thiago told Liverpoolfc.com post-match. "We are pretty happy with our performance most of the first half and [in the] second.
"First half was a great game. We concede a bit but we also created a lot of chances, we create good football and at the end we got the result [in the] first half.
"Second one, for sure we were playing with the time, with the result and also knowing that in three days you have another game, so it's a mix of feelings that you don't have to have. You just have to be focused on this game and stay hungry the whole game.
"We were preparing the game for [their] 4-4-2, 4-4-1-1, but at the end they changed.
"But I think we had a lot of experience in football to analyse the moment how the opponents are playing and just to convert our game there."
Liverpool's focus now quickly turns towards Wednesday evening's Merseyside derby with Everton at Goodison Park.
In the midst of a busy period in the campaign, Thiago insists the squad will approach the encounter with their local rivals like any other.
The No.6 continued: "It's a derby, it's always special. We have to have in our mind it's another Premier League game that we have to give [our] all. It's our mindset.
"It doesn't matter, it's a derby for the crowd. For us, it's just a game that we have to play now away.
"It's the moment of the season that we were waiting for, to play every three days, have less training for sure.
"But we want to play football. It doesn't matter if it's in one, two, three days, we just want to play football."