Steven Schumacher had no issue with Plymouth fans chanting “This is embarrassing” towards the end of a one-sided first half at Ashton Gate
Sam Bell fired City in front following a short corner after three minutes and five minutes later Matty James doubled the advantage with a close-range finish.
Adam Randall gave Argyle hope with a low 27th-minute strike from just outside the box, but Mark Sykes restored City’s two-goal advantage before the break from a Jason Knight pass.
Substitute Harry Cornick completed the scoring 10 minutes from time, shooting home from a Kal Naismith through ball, and Plymouth could have no complaints.
Manager Schumacher, who had made seven changes for the game, said: “Our fans were right to chant about it being embarrassing in the first half. I couldn’t believe what I was seeing.
“Four of the players who came in are regular starters and with the three youngsters making their Championship debuts, it was a case of if you don’t give them a chance, how do you know how they will do?
“Hindsight is a wonderful thing and on the back of a 4-1 hiding they don’t look great decisions. I knew I would take some flak if things went wrong.
“But it wasn’t only the youngsters who had a tough night. The whole team were off it from the start.
“What we learn from the game is that we have to be better. That was by far our worst performance of the season so far.
“We ask the lads before each game for a fast start and not to take any risks. Yet from the first minute today we were second to headers and then failed to defend a corner.
“It gives you a mountain to climb if you give away silly early goals.”
City assistant manager Curtis Fleming said: “We were as good or better in the first half against West Brom on Saturday, but not as clinical.
“It makes such a difference when chances are converted. That has been missing from our play in home games, but we have never lost faith in our processes.
“We got a bit sloppy at times and there is still room for improvement, but overall we are delighted.
“Not least we are buzzing about the impact of our substitutes in seeing out the game.”
Manager Nigel Pearson again watched the match on crutches because of a back problem.
Fleming said: “He is going to see a specialist, but he was okay to jump up and have a go at one or two of the lads when he wasn’t happy with them, so he can’t be too bad!
“He will be fine for what will be an emotional return to Leicester City with us on Saturday.”