"I went in and talked a little bit about what I saw, congratulated them on facing some tough adversity and winning, thanked them, and then proceeded to cancel the day off that they had tomorrow," he said after the Jets' 5-1 victory that snapped a five-game losing streak.
"It was good enough tonight but we can't rely on that being good enough in our next game. We've just got to get better."
It was his first night behind the bench after taking over from Claude Noel, who was fired as the Jets struggled lately to beat even teams below them in the standings.
The Coyotes (21-15-9) don't fit into that category although they too have struggled recently after a strong start. They opened the season at 14-4-4, have gone 7-11-6 since and Monday was their third loss in a row.
"It can't get much lower and we have to get better," said captain Shane Doan.
"It seems that we find new ways (to lose) every time. We haven't really had an issue with discipline so far this year with penalties and this time we did. You can't create much offence when you're shorthanded."
Phoenix handed the Jets eight power plays, although with one of the worst records in the NHL with the man advantage Winnipeg only managed to capitalize on one of them.
Fans who have been booing the lacklustre play of the home team lately were on their feet cheering and clapping for much of the game.
They didn't even wait until the game started to show how they felt about the coaching change. Maurice got his first cheer during the national anthem when his face showed on the scoreboard.
"It's a whole lot nicer being on the home bench when you win I'm sure, but it was a very special moment for me in my career and I'll cherish it," said the coach.
Olli Jokinen, Eric O'Dell, Blake Wheeler, Michael Frolik and Devin Setoguchi scored for the Jets (20-23-5), who outshot the Coyotes 38-19.
Oliver Ekman-Larsson scored for Phoenix but it was the only shot Ondrej Pavelec would let in and he won praise for his play from his new coach.
"I felt safe with him," said Maurice.
Ekman-Larsson scored on the power play at 12:16 but the Coyotes didn't have much time to celebrate.
"They did the one thing that we had talked about," said Maurice. "That when adversity came to the door, that next goal was huge."
Jokinen batted a behind-the-net pass from Dustin Byfuglien past Mike Smith at 12:52 to tie it up and then O'Dell scored his second of the season as he dashed in to snap in another at 18:00.
Thanks to four power-play opportunities the Jets outshot Phoenix 12-7 in the first period but both their goals were even strength. Winnipeg's power play is ranked 25th in the NHL.
The Jets kept up the pressure in the second until Wheeler backhanded Mark Scheifele's rebound past Smith to make it 3-1. At the halfway mark of the period the Jets had outshot Phoenix 9-1. They finished the game ahead 38-19.
Frolik made it 4-1 at 4:18 of the third when his angled shot beat Smith's glove.
Winnipeg's power play continued to be toothless until midway through the third when Setoguchi dropped to one knee as he slammed one past Smith and Byfuglien picked up his second assist of the night.
"To a man we did a good job of being ready tonight and playing the right way," said captain Andrew Ladd. "I thought we did a good job of getting a lot of pucks to the net and keeping it simple."
Setoguchi, who broke a goal-scoring drought that stretched back to Dec. 2, couldn't say whether the coaching change made the difference.
"I think everyone's work ethic was there and that's what gave us a chance to win the game," he said.
Notes: This was only the third time the new Jets have played the old Jets since the Atlanta Thrashers moved to Winnipeg, but with realignment they face each other twice more this season as part of the Western Conference.