The Reds have lost three matches during the winless streak and drawn four – including a 2-2 result against Sevilla to open group play on September 13.
Liverpool's last Champions League win came back in September 2014 with a 2-1 win against Ludogorets.
It has been even longer since the club last kept a clean sheet in Champions League play, with Tuesday's draw the ninth consecutive match the Reds have conceded in Europe's top club competition.
9 - Liverpool have not kept a clean sheet in the CL since November 2009 (vs Debrecen), conceding in each of their last nine games. Frail.— OptaJoe (@OptaJoe) September 26, 2017
Liverpool will hope to end both of their unwanted runs when they take on Maribor in their next group match on October 17.