The Reds have won all four of their opening Premier League games this season to leave them leading the way at the top of the table.
It will be a true test of the quality in Jürgen Klopp's side but Shaqiri is confident the Merseyside club can maintain their excellent start to the season.
However, the Switzerland worldwide has impressed during the global break with his national team and is expected to feature more prominently this month due to Liverpool's busy schedule of fixtures across various competitions.
The 26-year-old has played just 27 minutes in the league across two substitute appearances but with a series of tough fixtures coming up for Liverpool, Carragher feels that Shaqiri could be a crucial squad player - and hailed the transfer as a "brilliant buy".
"If whoever it may be needs a rest and you've got a game in the Champions League on Wednesday night, then a real big Premier League game on the Saturday, rest the player [in] the Champions League". You need to have a really, really good season to compete.
"As a United fan, that's a worry because it is still that mentality of "anyone but them".
"For me, Liverpool are one of the best teams in Europe, not only in England".
Harry Kane ran riot back then in October past year, scoring twice and forcing Klopp to substitute Dejan Lovren after just 30 minutes as Spurs cruised to a 4-1 win. Sadly they didn't win a title but now we try to make a step forward and try to win titles. That's the most important goal now. We want to keep our performances the way they have been. "That has to be our aim", Shaqiri said.
On Saturday, Keita will hope to be restored to the starting lineup as Liverpool take on Tottenham Hotspur in their next league game at Wembley Stadium on Saturday.