Conor Chaplin's first Premier League goal looked to have finally ended Town's search for a first home victory of the season.
But late goals from Cherries substitutes Enes Unal and Dango Ouattara inflicted an agonising defeat on the Tractor Boys.
"It's a devastated dressing room today," said Town boss McKenna.
"There were so many good things in the game and the performance. Some of our play was really good, right up to their first goal. It's a really disappointed group.
"We felt like we were defending well and looked like we could get a second goal. We were in control, and a really poor first goal from our point of view changes the momentum.
"I don't think we got what we deserved from the game, but that's football. I believe we will be back fighting next week.
"I certainly don't feel it's not meant to be, but I do feel we should have more points than we have. But it's not time to feel sorry for ourselves."
It was not the first time Andoni Iraola's side have staged a spectacular late comeback this season.
In August they trailed 2-0 at Everton in the 86th minute and went on to score three late goals for an unlikely victory.
"I think it was a game we didn't deserve to lose," said Iraola. "We missed clear chances to score in the first half and the beginning of the second we were pushing, and then you start thinking it's maybe not going to be your day.
"Ipswich were defending very well, not giving us a lot of chances. We needed fresh energy and fresh minds from the subs."
The victory moved the Cherries up to eighth but Iraola is not dreaming of Europe just yet.
"I think we shouldn't look at the standings right now," he added. "It's very early in the season - I don't even know where we are, just that we have 24 points.
"You can take a picture of the standings if you want, just in case we're not there, but I won't look too much.
"I am confident in this team because we are being competitive. Let's hope we can continue playing the same way.
"We have to get ready for a very busy period at Christmas and keep earning points and try to continue like this."
Ipswich have confirmed a medical emergency occurred in the directors' box after the match but have yet to provide any further details about the incident.