Tyler Dibling struck for Saints on five minutes before Sam Morsy scored Ipswich's equaliser in injury-time.
"It’s an enjoyable moment, I have to say,” McKenna said. “I think it was a hard-fought game. I think on the balance of play we probably deserved a point.
“I thought we did deserve a point on the balance of play and it’s a great way to get it, to score late in the game away from home against a team, who are fighting for their first win and had great energy from the crowd, were showing resilience in their way as well, to keep pushing as we did.
“Of course, we had the big chance with George (Hirst) just beforehand where the goalkeeper made a terrific save, but to bounce back from that, go again and then for Samy to get the equalising goal as captain in front of the away supporters, it’s a fantastic time to score.
“It’s big for us as a young group, as group that’s coming together in a new division, to go through an experience like that after the experience that we went through last week as well, to know that we can score late in the game, to know that.
“To have the belief that we’re capable of scoring late goals has been a big, big part of our story and for our new group of players and the new group coming together, mixed with the players that we’ve had here.
“To go through that together away from home in a goal like that, that’s a fantastic experience for us.”
Southampton goalkeeper Aaron Ramsdale threatened to keep Ipswich at bay, but McKenna said: “He made a couple of really good saves. But, I was really hoping that the group would get the goal because I know how important those things can be.
“I know how we’ve built that over the last couple of seasons, to become a team who have regularly scored late goals, who scored late goals in big moments in big games.
“I was really hoping for the group that they would get that experience today. Of course, it’s a point, but it’s much too early in the season for us to be thinking about tables or points.
“It’s a fantastic experience for the group to go through and I always believe in these boys that if they keep doing the right things, keep following the plan of how we chase games late on, then we always give ourselves a great chance to get a goal.
“It is, three games, two of them away games, each game a challenge, as they will be with their own story.
“To be as competitive as we have been, to show the different qualities that we have. Last week a very different point from this week. Last week, defending late in the game and trying to see out the point, today pushing for the equaliser late in the game and trying to chase the point.
“To go through those things and for it to be three games in a row that we’ve picked up results, that’s a big positive, and everyone knows who the opponents were in those first two games.
“We know we’ve still got a lot of improving to go. There were some good things today, there were things that I think we will definitely be better on in the course of time.
“But while we’re building our execution in all the phases, building the foundations of a successful group, most importantly never giving up and showing resilience whenever you need to.
“We’ve done those things over the last couple of weeks and it’s always nice to get something from your away games.”