The England international, who joined the Reds from Southampton during the summer, was named captain of the side for Tuesday night's League Cup third-round encounter with Middlesbrough.
Lambert was replaced in the 74th minute at Anfield, however, following a frustrating night in which Liverpool eventually prevailed on penalties.
"I wasn't expecting it, and it was a great honour to lead the team. It was a nice surprise," BT Sport quotes the 32-year-old as as saying when asked about the captaincy.
"But forgetting about that, it was a strange game. I wasn't happy with my own performance, so that overshadowed the honour of being captain a little bit. I didn't feel as sharp as I want to feel. That's the main thing I want to look at going back into training.
"I want to get my match fitness up because obviously everyone knows I'm not playing every game so I have to adapt myself now. I think I'm going to have to do more so my fitness is up to the same level as everybody else."
Liverpool return to league action this weekend with a crunch meeting against Merseyside rivals Everton.