Inter came from behind at San Siro despite Matias Vecino's 18th-minute red card following Douglas Costa's opener, Mauro Icardi and an Andrea Barzagli own goal giving them the advantage.
Although Juve were poor in the second period, a Milan Skriniar own goal drew the defending champions level with three minutes to go before Gonzalo Higuain nodded in a Paulo Dybala cross to earn a dramatic victory.
Inter therefore missed the chance to move into the Champions League qualification places but Spalletti said his team's defeat was not a fair reflection of the match.
"The easiest thing is to tell them [the players] the truth," Spalletti told Mediaset Premium .
"Clearly, we need to shake off the bitterness of this defeat, because the team didn't deserve it. The question then is why does this have to be forced upon us? That's the difference.
"It's difficult to make them accept it, because the problem is that you must give the players the credit they deserve. This is the game that means a lot for us, for the fans, for everyone. It'll take more than one sleepless night to shake that off.
"There are some things we don't understand… it should not have ended like this. It's upsetting, because the players are not some emotionless robots who only do this for work."
Referee Daniele Orsato drew the ire of Inter's players throughout. The official sent off Vecino following a VAR review after originally booking the player for a stamp on Mario Mandzukic, while Miralem Pjanic appeared to be lucky to avoid a dismissal after barging Rafinha when on a booking.
Juve's opener also survived a VAR review with Blaise Matuidi seeming to brush Juan Cuadrado's cross with his arm, although Massimilano Allegri's men had another goal ruled out for offside following the use of a video replay.
"It's difficult for me to evaluate," said Spalletti regarding the officials' performance. "I don't think there was a completely balanced treatment of situations.
"We above all lost because we used up a lot of energy by playing with 10 men. At the end, that equaliser for 2-2 was so chaotic and unlucky. The team deserved a more fortunate outcome, quite frankly."