Conor Chaplin's goal had the Blues on course for their first home win of the season, but AFC Bournemouth struck twice at the death - in the 87th and 95th minutes - to take all three points back to Dorset.
"It's a devastated dressing room," admitted McKenna, whose side are now four points from safety following three single goal defeats in the space of eight days.
"I thought there were so many good things in the performance. The commitment levels were outstanding and some of our play was really, really good, right up until the point of their first goal really.
"It's a really disappointed group because we felt like we deserved to take the lead and felt like we had a second goal that was harshly overruled.
Sam Morsy and Jack Clarke react after the final whistleSam Morsy and Jack Clarke react after the final whistle (Image: Steve Waller) "It was always going to be a difficult second half, especially with the quality of subs that they're bringing on, but I felt like we defended well, had chances to get the second goal and, on 86 minutes, I think we were in as much control of the game as you can be at 1-0 against a team of that level.
"There wasn't a huge threat and we were defending well, but a really poor goal from our point of view changes the momentum. They then have the momentum and the quality to execute really well for the second goal.
"It's an extremely disappointed group because I don't think we got what, on an individual or collective level, we deserved from the game. But that's football.
"As much as it's a devastated dressing room at the moment I know what the reaction will be. I believe in what the reaction will be. I believe we'll be back fighting next week."
This is the third time this season that Ipswich have dropped points in stoppage-time following on from late goals conceded against Brentford and Leicester.
"There's certainly not a feeling of 'it's not meant to be' or anything like that," insisted McKenna, whose side are now preparing for a trip to 19th place Wolves next Saturday.
"We feel like we could have had more points than what we have. Even by rights of being competitive in almost every game then you think you give yourselves a great chance to come out on top in the margins (more than we have).
"But it's not time to feel sorry for ourselves. We need to work. We need to keep trying to push our level.
"The boys are improving. Look at some individual performances. I'm sorry, but Cameron Burgess, Jack Taylor, Conor Chaplin - to give three examples - are lads who have gone from League Two to starting in the Premier League.
"The players know that so much good work is going on, but we need to own what we can own and keep trying to improve in every way we possibly can - to go and get a second goal and open up a margin, and own the mistakes we made late in the game.
"It's not (bad) luck. It's things we can do better. It's also a very, very, very high level of opponent who are going to chase the game with top quality forward players."