On a night where the Rams could not believe their misfortune in front of goal at iPro Stadium, Nigel Pearson's side saw their losing streak stretch to three matches.
Wilson saw an early effort blocked before he was just inches from getting on the end of Matej Vydra's saved effort.
A late first-half left-footed attempt from the 20-year-old was cleverly kept out by Bialkowski before Wilson was replace by the experienced Darren Bent on 64 minutes.
The United youngster has now made two starts and one substitute appearance for Nigel Pearson's Derby since arriving on a season-long loan in the summer.
The Rams currently sit 20th on the Championship table with just five points from seven matches.
Regarding Ipswich's loanees, Everton striker Conor Grant started and played the first half before being hooked for match-winner Luke Varney while Leicester City's Tom Lawrence replaced Kevin Bru at the break as Mick McCarthy rang the changes.