Gustavo Varela gave Monza an early lead from the penalty spot, but Tommaso Pobega equalised with a superb volley before Federico Bernardeschi converted a second-half penalty to complete the turnaround. Monza had the opportunity to rescue a point late on, but Lukasz Skorupski saved Patrick Cutrone's spot-kick.
Palladino was pleased with the progress his side are making, although he felt the quality of the contest had been affected by the officiating.
"It's a shame about the refereeing because it could have been a more enjoyable match. Instead, it became a messy game because the players were influenced by the decisions," he said.
"When players from both teams are complaining, it means something is not right with the officiating. Nevertheless, we have improved because we conceded little from Monza and played with our qualities and principles.
"We finally brought a victory to our supporters. I dedicate it to them. We were happy, and celebrating beneath the stand was wonderful. We can still improve and must continue like this."
The Bologna coach was particularly satisfied with his team's work in possession and their ability to attack space.
"I'm happy with both phases of my Bologna team. We have to play with one or two touches and attack the spaces. We also had a lot of possession, so we are becoming a more complete team."
Skorupski's late penalty save proved decisive, and Palladino was quick to acknowledge the goalkeeper's contribution.
"I'm happy for him. Today he saved us, and it is thanks to him that we achieved victory. We thank him because he deserved a win like this."
Monza coach Ivan Juric, meanwhile, blamed defensive mistakes and a lack of experience for another damaging result.
"We suffered against Bologna's direct play and their verticality. We were punished by mistakes from set-pieces. We gave away corners and lacked physicality in certain situations. Today we conceded two goals from set-pieces," he said.
"My players are paying for their inexperience. We have a very young squad, and we lack a lot of the experience needed to get results over the line."
Juric also defended his decision to make substitutions after Varela had been withdrawn, meaning the forward was unavailable to take Monza's second penalty.
"After 70 minutes, I made changes because the players had worked very hard. I find it difficult to answer whether I regret taking Varela off. We have to accept that inexperience is something you must take into account when you have such a young team."
The Monza coach also questioned his side's inability to deal with Bologna's long balls and second phases.
"We did not get to the second balls and that led to free-kicks and corners. We ended up defending too deep. My only regret is that we did not manage to get our own game going when we recovered possession."