Dyer was a former team-mate of Magilton and has backed the Irishman to be a success at Portman Road if he is given time by owner Marcus Evans.
Dyer, now at West Ham, told Ipswich's official website: "I've been to a few games this season and obviously it's not gone as planned, but he's brought in a number of players and it always takes time for players to gel.
"He may have had his doubters but I'm not one of them. I'm definitely behind Jim. A lot has happened at the club over the last year or so and I think the time to judge him is next year, not this one.
"The owner seems to be behind him and hopefully he will remain that way because I think Ipswich will reap the rewards over the next year or two."