Wirtz, who arrived at Anfield from Bayer Leverkusen last summer in a deal worth £115M, had a mixed start on Merseyside as he divided fans and attracted much criticism from pundits.
The 23-year-old grabbed seven goals and 10 assists from 49 appearances across all competitions for the Reds who finished the season trophyless under former manager Arne Slot.
Wirtz failed to score in his first 22 Liverpool appearances and as the new campaign approaches, he will be seeking to hit the ground running ahead of the first clash against Newcastle this Sunday.
Speaking to The Telegraph, Carragher says Wirtz must find success this season, or it may become embarrassing for Liverpool.
“Florian Wirtz faces a make-or-break season, but more is at stake than his Liverpool career as he belatedly seeks to establish himself in the Premier League.
"English football needs Wirtz to succeed as much as Andoni Iraola, the new coach at Anfield... How Wirtz fares at the start of this season will indicate whether he will be viewed as the right signing in the wrong era for Liverpool, moving to Merseyside just as the Premier League’s preferred style reverted to set-piece dominance.”
Carragher continued: "Failure to do so would embarrass the club that invested so much in a footballer they presumed to be a symbol of a golden future, and more than probably continue the trend of highly rated attackers believing Spain and Germany a better fit for their abilities."
In two Bundesliga campaigns, Wirtz delivered 21 goals and 23 assists for Bayer Leverkusen. If he can deliver that form for Liverpool then the side could be ready to fight for the title as fans wait to see what he can bring against the Magpies.