Gabriel Agbonlahor's first-half strike was enough for Paul Lambert's men to seal a surprise victory at Anfield, and Lallana, who made his Reds debut in the reverse, accepted that the result was a poor one.
He told the club's official website: "The lads are down and we know we've got to bounce back.
"It was very disappointing. We saw a couple of results earlier and we wanted to get the win to move closer to the top of the league.
"We're thoroughly disappointed but we've just got to recover well and go again on Tuesday night."
Lallana signed for Liverpool from Southampton for around £25m in the summer.