The Madrid job became vacant when Zinedine Zidane resigned as coach after winning a third consecutive Champions League title last May, and Pochettino, 47, said in an interview with El Pais published on Wednesday that he was offered the role.
"It was a difficult situation because the dream of any coach was at stake -- coaching one of the biggest clubs around. And I had to say no, that was tremendous," he was quoted as saying.
"It created a conflict because you know that if a coach wants to leave, he will leave, but I had just signed a new contract with Tottenham and I felt that I couldn't do anything."
Pochettino joined Spurs in 2014 and is one year into a new five-year deal at the club who have moved into a new stadium.
Julen Lopetegui was eventually named Real coach, a decision which saw him sacked as Spain manager on the eve of the 2018 World Cup, but he was fired by Real at the end of October.
Santiago Solari then took charge of Real until he was sacked in March, when Zidane made a sensational return to the club.
The Frenchman signed a deal with Madrid until 2022, meaning Pochettino may have to wait some time before he is offered another chance to coach the 13-times European champions although he said he did not regret turning Madrid down.
"Daniel Levy (Tottenham chairman) didn't want to accept the offers to free me from my contract so I would have had to have broken the contract and I couldn't accept that because I couldn't behave like that," he said.
"If my chairman thinks I'm going to stay, I'm not going to do a runner. Those are not my values. Why should a club sign a coach who does not keep his promises?"
(Reporting by Richard Martin; Editing by Ken Ferris)
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