James Beattie's gave Sheffield United the lead and he ended his own seven-game goal drought with a first-half header.
But Alan Lee struck nine minutes into the second half to earn the home side a point.
"We started pretty brightly and moved the ball well but the fact we didn't get an early goal gave them confidence," Magilton said.
"They began to get a foot hold in the game and we gave the ball away too cheaply for their goal, which was poor from our point of view.
"In the second half we showed a lot of character and I thought we'd go on to win.
"Overall it wasn't a game for the purists. I can't fault our effort but we lacked a bit of composure and quality and just didn't have enough in our locker.
"We had the capacity to hurt them but just didn't have enough craft or guile and looked a bit leg weary at times.
"But we'll move on and take a point against probably the most underachieving side in the Championship."
The draw was a blow to Ipswich's play-off chances, especially as rivals Plymouth won 4-1 against Colchester United.
Sheffield United worked hard and deserved to be in front at the break, courtesy of some generous Ipswich defending.
Town's Dan Harding tried to beat his man and duly lost possession near his own corner flag, drilling the ball straight at David Cotterill.
The midfielder fed Michael Tonge, who advanced deep into Ipswich's area before delivering a perfect cross to Beattie.
The former Everton striker was lurking unmarked at the far post and had the simple task of nodding home for his 14th goal of the season and first since Boxing Day.
The second half started in lively fashion with two efforts against the woodwork in quick succession. Tonge smashed a long-range effort against the bar and then, at the other end, Gary Naysmith headed against his own post for United.
The hosts were on level terms almost straightaway when Jon Walters won the ball after a throw-in and cross to the far post, where Alan Lee was waiting to steer a header beyond Blades goalkeeper Paddy Kenny.
United boss Kevin Blackwell said: "I came very close to getting my first win. It's been a tough start but the players responded brilliantly after losing 2-0 against Charlton on Saturday.
"We were abject in that game but much better tonight and we knew we had to compete otherwise we'd get rolled over.
"I was very pleased with the players' attitudes after questions were asked at the weekend and we maybe edged the game slightly."
Meanwhile Magilton confirmed that he has ended his interest in loan target David Nugent.
He had wanted to get the Portsmouth striker in for the rest of the season but said the deal is now "dead".
Sporting Life