In a scrappy, stop-start game of few chances, Chris Wood's converted spot-kick early in the second half proved the difference. Jota Silva took a dramatic tumble in the box after Sammie Szmodics' challenge.
"I've not seen it back closely," said McKenna. "But we have to own our part. You can't lunge in from behind in the penalty area. We had the box well covered, we had plenty of people in the frame of the goal and it's not a particularly threatening situation.
"It was a really tight game where it felt like the first goal was going to be decisive. We had opportunities to get it in the first half, we didn't manage to, but we felt in the second half we had it in us to step up another level. But then we gave away a penalty really early in the half that ends up deciding the game.
"Away from home especially, we shouldn't give the referee a decision to make there. It ends up being the decisive moment in the game."
Town's winless run at The City Ground has extended to 15 matches now (L9 D6), with this result seeing the Blues slip to 19th in the Premier League table ahead of Tusday night's home game against Crystal Palace.
"We competed pretty well," said McKenna. "It wasn't a particularly high quality game. There wasn't a lot of flow to it. Both teams felt like they were a threat when they got to the opposition's box. We felt like we were a big threat out to the righthand side in the first half.
"But it wasn't a game of great flow and neither team created an awful lot from open play. Set-pieces and being really disciplined can make the difference on days like today. We didn't manage to score from the set plays we got and we've given a pretty soft goal away from our point of view."
The home crowd got increasingly nervy in the latter stages of this game, but Ipswich huffed and puffed in an attempt to break down a low block.
"We didn't work the ball well enough," conceded McKenna, when asked about the period. "We had some momentum, some pressure. They're a team who are really hard to create clear chances against, especially in that phase when they went to five at the back with some big centre-halves who defend the frame of the goal well.
"But we didn't sustain the pressure well enough and work the ball to good enough areas. That last part of the game we can work towards doing a bit better on."
He added: "We're frustrated because we wanted to get something from the game. On the balance of play I don't think anyone could have had any complaints had it been a draw. I don't think you can say we did enough to win the game, but I think it was competitive enough to say that a draw would have been an even result.
"We were competitive in the first half, we were a threat. I don't think we hit our absolute best levels, but you can't do that all the time. I don't think it was a fantastically high quality game, but we were right there, looking a threat and defending with pretty good organisation after the first few minutes.
"We feel that we're in games and competing. To do that you have to be doing some things well, but we also know that to win games consistently there's another step to take. We didn't manage to make that step today."
Meanwhile, the Blues boss said that Axel Tuanzebe had to come off with a hamstring injury in the latter stages, the severity of which is yet unknown.
He also confirmed that the fit-again Jacob Greaves was just left out of the squad as part of his usual policy of not having centre-backs on the bench.