Shaqiri was one of the five changes for the Reds as Klopp's side blew away their local rivals on Wednesday night.
Divock Origi gave Liverpool the lead before Shaqiri added an excellent second with a well-timed run and finish across Jordan Pickford.
Michael Keane pulled one back for the hosts before Origi and Sadio Mane steamed the Reds ahead. Richarlison scored another just before half-time before Gini Wijnaldum rounded off the scoring in the 90th minute to give Liverpool a 5-2 win.
It was Shaqiri's first start for the club in seven months and his first goal since Boxing Day last year, with the 28-year-old putting in an impressive performance considering the time he's had out of the side.
"[Seven months] really? Sorry Shaq! He was injured a couple of times," Klopp said when asked about Shaqiri's involvement tonight.
"If he could have scored two goals like Divock instead of one, I could say exactly the same as I said about Origi.
"He looked completely fresh, he looked strong, physically strong, so it is important players train after they get injured.
"He had twice this calf thing this season, so there was not a lot to change but I think he has been back in training for two or three weeks now completely normal.
"He understood the situation, that’s how it is in a squad when you win a lot of games, you don’t make 20 changes.
"It was always clear this period now of the year is where we need all of the boys and I hope they will then be in the shape like Shaq and Div tonight, or Adam [Lallana] tonight.
"It’s really important and gives us the feeling that we can do it more often – and we will do it more often.
"It was an incredible performance, the set-pieces were outstanding. It was all really good. More to follow!"
Shaqiri will undoubtedly play a more significant role in the upcoming festive period, which sees Liverpool play ten games over the next four weeks.
The Reds hold an eight-point lead at the top of the Premier League table as they travel to the Vitality Stadium on Saturday afternoon to take on Eddie Howe's Bournemouth.