McKenna also had plenty of praise for the 3,000-strong away support, with Ipswich holding a 2-0 lead at halftime before Chelsea managed to fight back.
“I think the reaction was deserved and I thought the players and the supporters did themselves proud,” said McKenna.
“We knew it was going to be a really difficult game. We knew we were coming into it in a challenging situation, not just league position and stuff like that, but availability and injury, and playing against a fully motivated and almost full-strength Chelsea, so it was always going to be tough.
“The scorelines didn’t always go with the flow of the game. In the first half, we certainly weren’t at our best with the ball and it probably looked like there was a bit of nervousness in there at the start of the game.
“But we were really, really clinical, took our moments fantastically well, executed in the areas that we wanted to execute in the game plan and we defended with a lot of resilience and probably a little bit of luck, to be honest.
“In the second half, I actually thought we played better than the first half. We had more chances and for lots of the second it was a pretty even game with both teams pushing for the goals.
“We were disappointed to concede right from kick-off (in the second half), that was a big setback, but I think the response to it was very, very good.
“And from that moment, where it could end up a really, really difficult second half, it was actually, until (Jadon) Sancho’s goal, a pretty even second half and we looked as likely to get our second goal as they did their second goal.
“Of course, a brilliant moment from Jadon to score and make it 2-2 and then both teams were going for the win.
“It took a couple of great saves from Alex Palmer, to be fair, but we had our moments going up the other end.
“It was a really good game and the players gave everything to it again and I think they can be proud of their efforts.”
McKenna insisted a point was fair for both teams: “I think Chelsea had the better chances over the game but I think that was always going to be the case.
“But I think for the number of chances we created and the quality of our chances for an away team, I think we deserved something from the game, and we could have won it at the end, we could have lost it at the end.
“I think for us to compete with Chelsea as we have over the two games is testament to the group.”