The Lions enjoyed the better of the opening half-hour, with Chris Wood heading a great chance over while Town goalkeeper Stephen Henderson denied Andy Keogh, Liam Trotter and James Henry.
But two goals from DJ Campbell, either side of a simple finish from Daryl Murphy, made Jackett's men pay for their earlier profligacy.
Jackett said: "We should have been a goal ahead. Their keeper has made three very good saves and we've had an onside goal disallowed.
"We could have been one or two up in that period, but instead we found ourselves 1-0 down.
"Ipswich had an intensity but we needed that goal in the first half to give us something to build on.
"The start of the second half was poor for us. Two poor goals took the game away from us.
"We've been defending very well, but Murphy and Campbell were a handful for us and made key contributions for Ipswich.
"We kept going and battling but couldn't quite make a breakthrough, to get back in the game."