The Denmark international voiced a desire to pursue a new challenge after the Champions League final in June.
Eriksen's admission prompted links to Atletico Madrid, Juventus, Manchester United and Real Madrid, but a move failed to materialise before the end of the transfer window.
Interest is sure to be reignited when the playmaker enters the final six months of his contract in January, though Pochettino is not worried about his commitment to the cause.
"He's happy, he's always been happy," the Spurs coach said.
"Of course, everyone has aims and challenges and goals. I said before the Arsenal game he was in the right frame of mind, that's why I selected him.
"He's an important player for us, a player we appreciate a lot. His qualities are there and are important for the team. He's happy.
"Whether he plays is not because there is one year or less than one year on his contract. Always the decision is based on performance. We felt he was in the right place to compete."
Eriksen started and scored in the 2-2 draw at Arsenal and will have an important part to play in the weeks following the international break, with fellow midfielder Giovani Lo Celso ruled until the end of October through injury.
The Argentina international sustained a hip problem in a friendly against Chile in the United States, his first start of the season for club or country.
Spurs had been careful with easing their loan signing into the new campaign following his involvement at the Copa America, but Pochettino refrained from criticising the Argentine Football Association.
"The reality is we are all disappointed," Pochettino said. "The first, of course, the national team of Argentina. We're all really sad.
"We cannot change the situation. That is why it is so important to have good relationships with all the national teams. The situation is not to blame someone.
"It's bad for the player and our priority is always to try to anticipate the problems."
Tottenham could regain Tanguy Ndombele for Saturday's match against Crystal Palace, but Davinson Sanchez is in doubt with an ankle issue.