A header from Nunez in the 22nd minute was enough to hand Liverpool all three points against West Ham courtesy of a 1-0 win.
The Uruguayan, who Liverpool splashed the cash to sign in the summer, completed just under an hour of the game before being replaced by Harvey Elliott.
Reds boss Klopp was pleased to see Nunez open his Anfield account and believes there is much more to come from a player that the club are hugely excited about.
“He was outstanding. He is a massive talent and is only 22”, Klopp told Match of the Day.
“He came from Portugal and he wasn’t there for long, so not too long away he was [in] Uruguay.
“He is a really big talent and we’re really excited about him.”
Klopp also admits that he feels Nunez could even have gone home with the match ball.
“We scored a wonderful goal and with a bit more Darwin could have had a hat-trick”, he added.
Liverpool have now won back to back games in the Premier League and next face Nottingham Forest.
