Deje Elerewe headed the hosts in front at a corner just before half-time, but substitute Ben Johnson netted a rebound finish to get the game level after the break.
George Hirst and Ali Al-Hamadi subsequently saw penalties saved in the shootout as the Blues found themselves on the end of yet another cup upset.
“We didn’t do enough first half to force the first goal and then they score from a set-piece, which we couldn’t afford to concede.
“Second half we created plenty and but for a couple of near misses and a couple of good blocks we’d be talking about a good comeback win. There was a big, big chance in the 94th minute (that Ali Al-Hamadi missed).
“We weren’t clinical enough, it goes to penalties and we can only congratulate Bromley.”
Town started their season by snatching a draw at Birmingham last Friday night, McKenna admitting after that game his side needed to play a lot better if they were to live up to their Championship promotion favourites tag.
Speaking ahead of Sunday lunchtime’s home clash with Southampton, he said: “We’re still working into our rhythm as a team. We’re not quite there yet.
“There’s work to do at both ends of the pitch. We are where we are and are not the team we want to be yet. I believe we will be though if we stay on the right track. We’re certainly a work in progress.”