Campbell, alongside Craig Noone, came off the bench at half-time on Saturday and the pair combined to provide the winning goal for Cardiff, who progressed to the fifth round of the competition for the first time in four years.
The duo had been the heroes of the last round, both coming on and scoring in the 2-1 win at Newcastle United, and they were similarly influential again.
Noone's cross from the right led to a mistake from Bolton goalkeeper Andy Lonergan, which allowed Campbell to sweep the ball home from a tight angle to secure a 1-0 victory for the Welsh side.
After the game, Solskjaer paid tribute to the contribution made by his substitutes.
"Good players make an impact," he said. "And it was a great finish from Fraizer Campbell after a good run from Craig Noone.
"It was a fantastic, instinctive finish from Campbell. I'm happy with that.
"(In the) first half we did well in terms of possession but we didn't get many shots on goal. The changes made a difference."
Solskjaer also reserved praise for debutant Mats Moller Daehli, who came on in place of Joe Mason late in the game to make his first appearance since signing from Solskjaer's old club, Molde.
"Mats was terrific when he came on," the Norwegian said.
"He made an impact, kept the ball and had a few shots. He had a good 15 minutes."
