Cuper was sacked as Inter boss after an indifferent start to the season, to be replaced by former Milan manager Alberto Zaccheroni.
Some reports said that Cuper had lost the confidence of the dressing room and that the squad were not playing for him, but these have been dismissed by Argentinian international Zanetti.
"Not in any moment did we play against him," insisted Zanetti.
"Having read these things in papers bothered us.
"The situation is obviously not good if a coach is sacked but this is football.
"The club made this choice and we put ourselves at their disposal to be competitive. It's a difficult moment."
However, Inter president Massimo Moratti says that he had to take the decision to dismiss Cuper because his relationship with the players had deteriorated.
"It's a decision I took unwillingly. I'm sorry for the man and for the professional. Also, in the last meeting, he had very good behaviour," Moratti told Gazzetta dello Sport.
"There weren't the conditions to continue because the bond between him and the team was broken and there was no more the feeling that it's necessary to play well for him.
"So I took this decision for everyone's good. For Inter and for the coach, too."
Youth team coach and assistant boss to Cuper, Corrado Verdelli, will take charge for the club's UEFA Champions League clash with Lokomotiv Moscow.
Verdelli says that he feels desperately sorry for his former boss.
"I'm sorry for Cuper," said Verdelli. "I have talked to the players and I'm convinced that they can leave all the pressure and nerves from the last few days behind them.
"I didn't expect this job. It's a dream."
