The 23-year-old, who replaced £125m British record signing Alexander Isak at half-time after he had opened the scoring, quickly earned a booking for punching the ball away in frustration.
Five minutes from time, Ekitike then slotted home Federico Chiesa’s pass to restore Liverpool’s lead after Shea Charles had equalised.
His subsequent celebration, removing his shirt and holding it up for the cameras, prompted referee Thomas Bramall to issue a second caution and a red card.
This dismissal means the Frenchman will be suspended for the Premier League leaders’ trip to Crystal Palace on Saturday.
“Needless? Yes. And it was stupid. The first one was already needless and to a certain extent, stupid, as you have got to control your emotions,” said Slot.
“I told him that if you score in the Champions League final in the 87th minute after outplaying three players and hitting it in the top corner I can maybe understand. He is like, ‘This is all about me, what did I do’.
“But I am old-fashioned, I’m 47 and old. I never played at this level but did score a few goals and if I scored a goal like this, I’d have turned around and walked up to Federico Chiesa and said, ‘This goal is all about you, this is not about me’.
“It’s always the best to control your emotions. If you can’t, do it in a way that doesn’t lead to a yellow card.”
Ekitike apologised for his dismissal, saying emotion got the better of him.
He posted on Instagram: “I was so excited tonight to help the team achieve another victory here in our home for my first Carabao Cup match… The emotion got the better of me tonight. My apologies to all the Red family.”
The red card was the second low point as 18-year-old debutant Giovanni Leoni, who had enjoyed a trouble-free night, was carried off on a stretcher with a serious-looking knee injury and will undergo a scan to determine the damage.
“He is down because, for him, it didn’t feel good immediately. Normally the emotions of a player tell you a lot,” added Slot.
Amid all the late mayhem Isak’s expertly-taken maiden goal just before the break was almost forgotten.
“I should have scored earlier as well. It is part of being a striker, you miss some and score some,” the Swede told ITV.
“I feel confident in myself that things will work out and when I get chances I will put them away.”
Slot, joking that no-one mentions Isak’s transfer fee, added: “It is only six or seven days ago he made his debut so time goes so fast, but we got him not in the best circumstances in terms of match fitness (as he missed Newcastle’s pre-season).
“So the best moments will hopefully start when he comes back from the Sweden national team (next month) – then we can expect even more from him, but until now I’m very happy.”
Southampton boss Will Still at least saw the funny side of the red card for Ekitike, whom he had as a player at Reims.
“Hugo cracks me up. We caught up before the game and he said he would come on and score and give me his shirt and b****r off,” he said.
Still was frustrated his side did not help themselves.
“We had a massive chance, hit the crossbar, somehow not put the ball in the back of the net and 30-40 seconds they have gone up the other end and we have put it on a plate for them,” he said.
“It sums up our season so far. We seem to keep shooting ourselves in the foot.”
