Cole made his Liverpool debut on 5 August 2010 against Rabotnički in the UEFA Europa League assisting the opening goal for David N'Gog in a 2–0 win. His league debut, against Arsenal at Anfield on 15 August 2010, lasted just 45 minutes as he was sent off for a challenge on Laurent Koscielny. In his next match, on 19 August 2010, Cole missed a penalty against Trabzonspor in the UEFA Europa League third qualifying round first leg, though Liverpool still won 1–0. Cole played in Jamie Carragher's testimonial match, where he scored his first goal for the club. He then scored his first competitive goal for the club against Steaua București in a Europa League group stage match at Anfield on 16 September 2010, converting just 27 seconds into the game. Liverpool ended up winning 4–1. He scored his first Premier League goal for Liverpool in a 2–1 win against Bolton Wanderers on 1 January 2011. On 17 February, Cole played his first match under new manager Kenny Dalglish in a 0–0 draw against Sparta Prague in the Europa League, in which he came on as a first-half substitute for the injured Fábio Aurélio. Cole scored his first and only goal under Kenny Dalglish's tenure in a 5–0 win against Birmingham City at Anfield in April.