The Demons came out firing last week following news club president Jim Stynes had cancer and Bailey was rapt that his team could reproduce that strength at the contest to notch a second win in succession.
"The boys new it was going to be a real challenge this week coming off the emotional game of last week," Bailey said.
"It was always going to be a test [to see] whether we worked hard for each other without that external stimulus.
"I thought they did that for most of the game.
"Our tackling was still there, I thought our pressure was really good and that was the easiest thing for us to target from last week.
"We did that well last week and it was good that the players were able to replicate that. Maybe not the number [of tackles] but the attitude to tackling and pressure [was there]."
Despite several skill errors under pressure which threatened to bring the Dees unstuck, Bailey was delighted with the mental toughness his team showed in the face of a late charge by the Power.
In just his fourth game, livewire forward Liam Jurrah booted four goals in the 11-point win to cement his cult figure status among Melbourne fans.
"He's starting to come out of himself a little bit," Bailey said of Jurrah. "He's got a great personality, Liam, which will eventually come out.
"He's quiet, I suppose at the moment he's letting his footy do the talking, but he did some good things and he's coming off [almost] a zero pre-season base. He's got some exciting things ahead.
"He's added another dimension up forward for us, as has young Ricky Petterd; it was pleasing to see two young blokes take their chances and kick their goals."
The coach admitted to relief at his side lifting itself off the bottom of the ladder with the win and was confident his players would continue to reap the benefits from the back to back victories.
"We've got two wins [in a row] so their application has been great and it's just good to see the players smiling and building a bit of confidence and a bit of belief amongst them which is important," he said.
"I think what the last two weeks have shown is that when the boys have a crack and they're all prepared to do the hard things that builds a bit of belief – there's no doubt about that.
"Morale amongst clubs is important and a win like this will certainly add to that."
Daniel Bell will go in for scans on Monday on the AC joint injury he suffered in the third quarter of the match.
