Town had hoped to bring in the 22-year-old after he struggled to make his mark at Fratton Park, scoring just three goals in 16 appearances since his transfer from Preston North End last summer.
However, Magilton has now called time on his pursuit, growing frustrated at what he perceives as lack of respect from Nugent.
He told BBC Radio Suffolk: "Portsmouth have been very good about this, but we've spoken to the player and we haven't had a response.
"So David Nugent can go and play for whoever he wants now. The very least we deserve is a phone call or something to suggest he's not available.
"Premier League players who are not in their squads seem to choose the option of not coming out and playing.
"I was at a Premier League club and my self-satisfaction was zero if I wasn't playing on a Saturday, but the game has moved on and these lads seem quite happy to pick up their money and sit there and not play."