Michael Cronshaw scored Wrexham's goal to draw level after Ipswich took the lead. But it was the visitors who ran out winners with a late goal.
Wrexham: Vinny Whelan, Kia Edwards, Johnny Hunt, Lee Jones (River Cass 73), Chris Marriott, Tom Matischok (Robert Pearson 67), George Stewart, Matty Hurdman (Jack Jones 67), Michael Cronshaw, Mark Stewart (Obi Anoruo 73), Luke Carden.
"The boys didn't deserve this result," coach Steve Cooper told the official website.
"It was a shame we weren't able to push on and claim the win for ourselves, but I think we can take plenty of positives from the performance.
"I think we have shown we can play and have more than matched, in all departments, a team from a higher division.
"Things are starting to come together and we have demonstrated that we have some ability."