Leonardo Ulloa's quality first-half goal had put Brighton on course for not only their first quarter-final since 1986, but a mouth-watering home clash with Sunderland and former manager Gus Poyet.
However, Yannick Sagbo's strike five minutes from time snatched that away from them, earning the Tigers a 1-1 draw and taking the tie to a replay at the KC Stadium.
UEFA regulations mean the match will be replayed next Monday after important league games for both sides on Saturday, angering and perplexing Bruce.
"I find that ridiculous, I have to tell you," the City boss, whose side travel to Cardiff in the Premier League, said.
"Surely we could play on the same night as the Champions League, you would have thought.
"I think it is a UEFA rule, which reads nobody plays on the same night as the Champions League. We'll have to take it as it is and deal with it as it comes.
"It is quite a bizarre one, isn't it? For them to say to the FA that we can't play the same night as they are playing the Champions League.
"I don't think there will be many tuning out of Barcelona against Manchester City to tune into Hull versus Brighton, no disrespect.
"But there you have it, they think it's going to clash. Is it going to be a real problem for them? I somehow doubt it."
Garcia echoed those sentiments after the match, with Wigan heading to the Amex Stadium before Brighton head to Hull on Monday.
"I don't think it is good for anybody to play two games in three days, but it is what we have to do and we will do it," the Brighton manager said.
"Of course the travelling will not go in our favour. Now we have to start focusing on Wigan to try and win.
"For me, they have the best squad in the Championship, can play with three different starting line-ups and be fighting for the promotion places. We have to be focused on the next game.
"Of course it is not the best scenario for us, but the competition is like this."
It could have been so different had Albion held out for what would have been a deserved victory. Ulloa wasted a glorious chance to double their lead before half-time, but could have lost in the latter stages as Hull pushed on following the equaliser.
"I think in the first half we were the better side," the Spaniard added. "In the second half, the game was very even and we had the chances to win.
"But the game could have gone either way. I am really pleased with the performance of all my players, especially the younger ones.
"I think we had chances to win and when you concede late on, you can be a little bit disappointed.
"But my feelings are really good, I am really happy, not the final result but that my players can play in the Championship and most of them in the Premier League."
For Hull, the biggest positive from the match was the return of Sone Aluko. Making his first start after four months out with an Achilles injury, the 24-year-old forward played the full match and provided the assist for Sagbo's equaliser.
"He got better as the match went on," Bruce added. "I wasn't planning 90 minutes for him.
"I was speaking to him every 10 minutes and he was okay physically and it was his bit of magic that kept us in it.
"It will be good for him next Monday as well, so he can pencil that one in."