The Italian manager was furious that the former England striker's opener for Stoke City was not ruled out after he appeared to handle the ball on his way to scoring
The 31-year-old opened the scoring on the 15 minute mark for the Potters, but a debut goal from Javi Garcia twenty minutes later earned the visitors a point.
City’s players surrounded referee Mark Clattenburg after Crouch’s goal claiming the former England and Liverpool striker handled before finishing past Joe Hart, however the official was unmoved by their protests.
And, despite not seeing the incident himself, Mancini was insistent that the goal should have been disallowed.
“If you want to start with the first goal we should talk about the NBA not football,” the Italian sarcastically told reporters.
“I didn’t see from the bench but I saw all my players talk to the referee. The incredible thing is that the referee was behind Crouch.
“Sometimes it can happen when the handball is not voluntary but not today.
“We know that here is always difficult, not only for us but for all the teams, and we had two incredible chances at the end of the game and we are unlucky.”
Mancini handed debuts to three of his summer signings with Scott Sinclair, Maicon and Javi Garcia all featuring at the Britannia Stadium.
It was Garcia, a deadline day acquisition from Benfica, who equalised for his new club and his performance impressed Mancini.
“I think that Garcia played well,” Mancini added. “Like Maicon it was the first game for them and I think both players did a good performance.
“They don’t know their team-mates, they did well.”
Stoke boss Tony Pulis later admitted his side were fortunate with Crouch’s opening goal, but felt that their performance merited earning the rub of the green.
"I haven’t seen it [handball by Crouch] but they tell me it is, and I believe the ones who tell me, so I’ll take that on the chin,” he told reporters. “It’s nice for us, a smaller club, to have a decision against a bigger club.
“I thought looking at the major incidents we had the run of the ball today, but I believe we deserved it.
“The team worked so hard, we’re playing against one of the top teams in Europe, the players they’ve left out today, players aren’t even on the bench, it’s a phenomenal squad Man City have got.
"To compete with them you’ve got to play as one, and the 11 players out there today played as one, every player gave everything and it was lovely even to see the new lads like Charlie [Adam] and Steven [N’Zonzi] just give everything for the team.
"They showed with lots of effort and commitment you can get results against sides like this."
New signing Michael Owen came on in the closing stages to make his Potters debut, and Pulis thinks that once the former Real Madrid and Liverpool man is fully fit, he will be a real threat for his side.
“He’s trained ever so well over the last couple of days, he’s desperate to get going,” he added.
“He needs a lot more football, he’s done a lot of work by himself fitness-wise but playing games is a lot different from just running.
"We will try and do that [find space for Owen] as soon as Michael’s fit because we need goalscorers in the team.”