Luis Suarez with two goals and an assist won the game for LIverpool in a 20 minute spell in the first half.
Cardiff had managed to keep the home side out for the opening 25 mins and had created a decent chance when Craig Noone forced a quality save from Mignolet.
The moment Suarez volleyed the opening goal Liverpool ripped Cardiff to shreds. Suarez broke at speed to cross for Raheem Sterling to tap in.
Then Suarez showed his class again with another superb finish from just outside the box on the stroke of half time.
Malky Mackay, backed non stop by the Cardiff fans, sent his players out for the second half three minutes ahead of the Liverpool players and within 10 minutes of the restart had made two substitutions. Fraiser Cambell relaced Peter Oedemwingie and Kim Bo Kyung came on for Gary Medel and immediate Cardiff pulled one back.
Fraiser Campbell won a free kick wide right and when the cross came in Jordon Mutch was unmarked to head Cardiff's goal.
For the next 10 minutes Cardiff were in control and could have won a penalty as Martin Skrtel wrestled Steven Caulker. It wasn't the first time. Cardiff had at least three decent shouts for shirt pulling / obsruction.
Mutch headed over for another chance while at the other end Suarez hit the post and Marshall denied him his hat trick.
Apart from Liverpool's goals in the first half they also hit the post twice and had a shout ruled out by Hawkeye - the goal line technology.
Malky Mackay has retained his dignity and put in another professional performance.
After the match Malky praised the effort from his players. He told them at half time to be brave and play on the front foot.
Mackay paraised the supporters who were still in Anfield singing his name 30 minutes after the final whistle.
He ended his interview saying: 'I won't be walking away. I'm proud to be the manager of Cardiff City'
Losing at Liverpool today is not a major disappointment. It's the next two matches that are important. Southampton visit CCS on Boxing Day and bottom club Sunderland come to South Wales a week today. Victory in one of those games is essential.