An own goal from Forest skipper James Perch and a David Wright effort proved enough for the home side, with Nathan Tyson netting a late consolation for the visitors.
Magilton, who had faced calls to quit from fans and local media ahead of the game, admitted he was still finding his way in his third season as a manager but was driven on by criticism.
"It has inspired me even more to succeed," he said. "Criticism is part and parcel of the game and you have to learn to accept it.
"All I will say is it's a learning process for me and I'm going to use it for that. It's part of my early years in the job."
The Ipswich boss thanked the home supporters for their reaction to him and his side.
"I thought the crowd were tremendous for us," said Magilton. "When there was a lull tonight they picked us up."
He added: "I thank them from the bottom of my heart."
Ipswich faced a nervy final 13 minutes after Tyson's goal halved the deficit, with the visitors nearly snatching an equaliser when substitute Emile Sinclair hit the inside of the post in the 87th minute.
"It was a hard-fought win," said Magilton. "It was a scrappy win but it was a win nonetheless and, after three home draws, it was important to win a game of football and the players did that.
"What was important tonight was the result and I'm thrilled for them. We've showed a bit of character."
Forest manager Billy Davies felt his side had deserved a point out of the game.
"There were lots of positives in the second half and we probably should've sneaked a draw at the end," he said.
"The second half was much more positive."
Davies praised Ipswich's strike force of Pablo Counago and Jon Stead.
"I thought Ipswich's front two were excellent," he said. "I thought their work rate was excellent, their movement was excellent.
"You can just see the difference. We're asking a lot of our young players to play at this level."
Forest encountered Ipswich's Richard Wright in fine form, with the goalkeeper making a series of saves to deny the visitors.
"He made some good saves," said Davies. "He certainly done his job brilliantly."
Despite their defeat, Davies said he could take some positives from the match.
"There were a lot of good performances in the red jersey," he said.