Daniel Sturridge and Luis Suarez scored within the opening 17 minutes before Steven Gerrard netted his 99th Premier League goal with a penalty before half-time. Palace improved after the break and notched through Dwight Gayle.
Holloway felt their 3-0 half-time deficit was harsh, especially as he disputed the penalty awarded after Dean Moxey was adjudged to have pulled back Raheem Sterling.
"Having watched it again, I'm pretty upset. I thought he's made a mistake there," he said.
"Unfortunately, we are being punished for any singular mistake we make.
"Shape-wise we got it wrong for the first goal - I didn't want to leave three up, I wanted one of my front three to work back but we got that slightly wrong.
"The second goal was self-inflicted. I didn't think my centre-half (Adrian Mariappa) should have tried to win that (a challenge with Suarez which allowed Sturridge to run free).
"But that was probably our best spell. We had a couple of chances and unfortunately if you don't take them at this level it can be pretty unforgiving.
"It is not good enough but I didn't think we deserved to be 3-0 down on the balance of overall play.
"You have to keep trying and keep going and digging in.
"I thought the character in the second half was terrific but when you are 3-0 down you can relax and play a little bit and maybe Liverpool took their foot off the gas.
"But we actually won the second half and there was enough fidgeting by Brendan [Rodgers] next to me."