Dier had a call of nature in the second half of the fourth-round tie, which Spurs won 5-4 on penalties after it had ended 1-1 in 90 minutes.
Mourinho followed his player to the dressing room to hurry him along as Spurs were playing the match with 10 men at the time and was glad he did as the defender went on to score in the shootout.
Mourinho responded with humour when it was pointed out that rushing someone to go to the toilet can have the opposite effect.
He replied: “The problem is that was not a pee.”
Dier was selected 48 hours after playing in Sunday’s Premier League draw over Newcastle and Mourinho says the incident was a result of his extra workload.
“With Eric you can imagine what happened,” Mourinho said. “For him to leave the pitch it was easy to imagine what happened. He knew it, I was just pushing him to come back as soon as possible, because no more changes, and one player less is the consequence of something not human that he did, which was to play two matches completely dehydrated, tired, no energy in the muscles.
“Of course he is not playing Thursday because I would definitely kill him.”
Dier, who was named man of the match, tweeted a picture of a toilet in the Tottenham dressing room accompanied by the message – ‘The real M.O.M.’
Reflecting on his eventful night, Dier told Sky Sports: “After playing on Sunday and then tonight, it wasn’t easy. Maybe that was one of the reasons I had to run off the pitch in the second half.
“He (Mourinho) wasn’t happy but there was nothing I could do about it really. Nature was calling! There was a chance when I wasn’t on the pitch but thankfully they didn’t score.”
A long night looked on the cards as Spurs, playing without a recognised striker on the pitch, went behind in the 19th minute to Timo Werner’s first Chelsea goal.
But Mourinho’s men got better as the night went on and deservedly levelled in the 83rd minute through Erik Lamela, which sent it to penalties.
The first nine spot-kicks were successfully converted before Mason Mount missed the decisive one to send Spurs through to the quarter-final.
It gave Mourinho a first managerial win over Frank Lampard and the pair ended the night as friends, though it did get heated midway through the first half.
Mourinho took umbrage at his former midfielder chatting when the Portuguese appealed for a foul and offered him some advice, mixed in with a few expletives.
“With Frank the most important thing is my feelings towards him rather than any words we exchanged,” Mourinho said. “I owe him everything he gave me, he always gave me everything he had as a player and I never forget that.
“My feelings towards him will always be feelings of how much I owe him for how much of an incredible player, friend he was.
“The only thing I was telling him, just an opinion of an old coach to a young talented coach, which was when the players need us it is when they are losing, when they are winning we don’t need to be the protagonists of the touchline, we need to be there when they are losing.
“In the last match when they were losing 3-0 I felt really sorry for him because he was sad and quiet in his chair.”
Lampard brushed the incident off, however.
He said: “We were having some fun on the line. I get on well with Jose and I think he said that to me.
“I commented on the fact that he seemed to speak more with the referee than he speaks with his players so it is just a moment with us. I have a huge respect for Jose, no matter what he says on the touchline.
“I think he was feeling the sense of the first half and how it was. All was well at the end of the game and that will never change.”
