Liverpool edged into a fifth-minute lead in the second leg of their last-32 clash after James Milner finished from the penalty spot.
Philippe Coutinho and Jordan Henderson wasted the home side’s best opportunities to extend Liverpool’s advantage at Anfield as the Reds clung on for a 1-0 aggregate win.
The club’s former captain said that he would be worried if Jurgen Klopp’s side face one of the top sides remaining in the Europa League in the next stage.
“Liverpool know the first half was good enough but the second half and their inability to score the second or the third is a problem,” McManaman told BT Sport.
“They kept two clean sheets against Augsburg and the reason is because they’re not very good. They’re 13th out of 18 in the Bundesliga.
“You expect Liverpool to beat these teams and once they do progress, hopefully they’ll play better against better opposition.
“If they did meet a Borussia Dortmund or a Napoli, they’ll be beaten. They need to improve.”
Liverpool face Manchester City in the League Cup final at Wembley on Sunday afternoon.
The 18-time English champions haven’t won Europe’s second tier competition since Gerard Houllier guided the Reds to Uefa Cup glory in 2001.
Liverpool haven’t reached the last 16 of a European competition since 2010 when the Reds lost to Atletico Madrid in the Europa League semi-finals.
MORE: The latest football news