Conte highlighted Tottenham's ambition before the start of the season after Spurs had yet to spend during the transfer window following their runner-up finish to Premier League champions Chelsea last term.
The Chelsea boss also insisted that Tottenham not winning the title or qualifying for the Champions League is "not a tragedy".
Heading into Sunday's London derby, Pochettino – who made his first signing of the window following the club-record arrival of Davinson Sanchez – said Conte explained his comments.
"Last week, we had an opportunity to talk a little bit and he was very clear with me," Pochettino said.
"He tried to explain what he wanted to say and sometimes the headlines are not the same as what he wanted to say. He explained to me and it's not a big issue.
"I respect him and Chelsea and it's time to play and show we are better. It's always a challenge to play the champions."
Pochettino added: "He did not apologise, he just tried to explain things to me. It is one thing how he relates things to you, it is another how you perceive the message and translate it to the fans.
"Sometimes the difference is important, and he wanted to try to explain what it was that he had wanted to say. It was different to how you had explained it to the fans, and I got his message direct.
"I understood it when he explained to me. What he said did not upset me, it is only that he wanted to be sure that I had got the right message, not the wrong message. For me it is not a big issue.
"Every manager has a right to say in the media what they want. For me, it is not my job to judge what they want to say or how they give their opinion. I don't believe he wanted to be disrespectful to Spurs or myself.
"Conversation is good. We are colleagues and I think showing respect is important. In the Premier League we talk about fair play and everything, so it is important to show as the manager, we are being responsible every week in front of the media."