Erling Haaland scored a hat-trick and Antoine Semenyo was also on target as City piled the pressure on Liverpool boss Arne Slot with a big win.
It left Slot in a perilous position heading into Wednesday night’s Champions League quarter-final against Paris Saint-Germain, with Szoboszlai’s comments leaving little to the imagination.
"The fighting spirit wasn't there enough, the mentality wasn't there enough. None of us were there to be honest as much as we could,” said the Hungarian midfielder.
"When you do something and there is no result, it makes no sense. We had chances and missed them, we conceded an easy penalty. We lose 4-0. We cannot concede as much as we concede. Nothing else to say.
"It's hard to win here. After 1-0 down you still believe. At 2-0 down, it's our own fault to come in at half-time conceding in the last minute another goal. At 2-0 the chances are lower and lower.
"You come out and want to show we are able to come back and you concede a third one, from then on there is no more chance to come back."
"It's a hard time, but we have to stick together. On Wednesday there is another chance, but we have to get in our head this is not the season we would like to end.
"It's hard to find words to be honest. We wanted this one so much. You lose 4-0 at City and it's not the best."
Slot confirmed he will speak to Szoboszlai to clarify his comments, as he gave a bleak verdict on his side’s latest setback.
"It's very disappointing. Not only in the manner, but also the result and the score. Another big disappointment for us,” said Slot.
"What has been missing for large parts of the season, converting our chances into goals. I think it was an even game up until they scored the penalty and the last time we played here we conceded just before half-time and again today.
"We get a penalty and we get a chance but that doesn't tell me anything. The first 35 minutes was the sort of team I would like to see but the 20 minutes after that, we have to defend so, so much better than we were doing today.
"Not nice to go in at 2-0 just before half-time, not helpful for your mood, especially after the season we have had. That was really hard to take. The only good thing was that we didn't concede more.
"We have had a lot of setbacks and disappointments, but that is also part of being a football player and being a human being and you have to stand there when things are not so positive and that's what it is about now.
"Players that have shown so much quality in the past now have a fantastic chance to show that again against PSG."
Slot’s future as Liverpool manager appeared to be on the line prior to this heavy defeat, with rumours linking Xabi Alonso with a move to Anfield certain to intensify after this latest setback.