The Bluebirds were 2-1 ahead midway through the first half, but Liverpool were ruthless in front of goal and found the net four times after the break.
However, Solskjaer believes that Martin Skrtel's second goal, which was the away side's third, should not have stood as Cardiff had two players off the pitch.
"We're disappointed we didn't get anything. Our first-half performance was fantastic," Solskjaer told reporters.
"The performance once again was good. We feel hard done by with the third goal though, two of our players were off the pitch
"Now we turn to a big game with West Bromwich Albion next weekend. Teams around us lost today as well. We'll keep fighting."
Cardiff, who travel to The Hawthorns to face West Bromwich Albion next weekend, are 19th in the Premier League table, three points behind Crystal Palace.