But the Northern Irishman joked he would have "strangled" the 20-year-old winger, who made one goal and scored the other, if City had equalised in the Portman Road derby clash.
Ipswich came back from a goal down after falling behind in the fifth minute to a stunning 25-yard drive from City loan player Ched Evans.
The home side responded seven minutes later when Haynes crossed and Norwich defender Alex Pearce sliced into his own net.
Haynes, who was rejected by City as a youngster, then finished coolly after being sent clear by Pablo Counago in the 39th minute.
Town went on to miss a series of chances in the second half, with Haynes one of the main culprits.
"Had we not won the game, I would've strangled him," joked Magilton.
"For the first goal he got into the right area. It's a good ball and then a composed finish for the second.
"We had Danny at his best and worst. He is a threat. He is getting better every game.
"I've got a lot of faith in him. He needs a little finesse but, when you have got raw power and pace, the finishing touches take a little bit of time."
Magilton predicted his side would have a nail-biting end to the season as they push for a play-off place.
"I think it's going to the wire," he added. "I hope it does go to the wire because it means we are still in the hunt. Today was big for us."
Ipswich rose to seventh place following the win and are now one point off Crystal Palace in sixth.
City boss Glenn Roeder, whose team are only four points clear of the bottom three, refused to accept his side were in a relegation scrap.
"We've got nine points to play for and we will try to achieve all nine points," said Roeder. "We will stay positive.
"It's a disappointing performance, especially after we took the lead so early.
"We couldn't have asked for a better start but didn't get to grips with the game.
"It was a very lucky equaliser and that put us on the back foot. It was a very disappointing game for everyone at the club.
"Just recently, we went to Bristol City and ripped them apart and lost the game in the last two seconds. Today it was the same scoreline but a completely different game.
"We didn't put them under much pressure. We don't make excuses."
Sporting Life.