The Reds suffered a setback in their push for a top-four finish as they were kept at bay by a dogged Saints performance at Anfield.
James Milner came closest to breaking the deadlock but saw his second-half penalty saved by Fraser Forster at the Kop end.
Speaking after the game, Lovren could not hide his disappointment over two points dropped, but he promised a response from Jürgen Klopp's team.
LFCTV GO: Dejan Lovren offers his post-match thoughts
He told Liverpoolfc.com: "We could win today but football is unpredictable.
"We have, I would say, not problems against Southampton, but we can't find the goal. [It's] definitely a big disappointment.
"We need to keep going, to fight now [in] the next two games and to win."
The Croatian also absolved Milner of all blame for the result, hailing the No.7's record of seven goals from seven spot-kicks prior to yesterday.
He added: "Milly scored so many goals from penalty kicks this season and we almost needed it every time.
"You think, like all season, Milly will score [the penalty] but one time he needs to miss and that's today unfortunately. It happens to everyone."