The mid-table Lazio led twice but were pulled back, only for Paolo Cannavaro's 83rd-minute own goal to gift them victory.
The encounter was played in a strange atmosphere as Lazio fans protested against president Claudio Lotito.
While Reja said he wanted to see a united Lazio, he understood the supporters' right to have their say.
"We played under a lot of tension in a bizarre atmosphere. This is very strange and doesn't happen every day," Reja told Mediaset Premium.
"The lads put in a great performance, especially in terms of character. They really wanted to win this game and I have to compliment the team.
"I don't know what the situation is with the ultras. Of course it would be nice to see the fans, team and directors form a single entity."
Stefan Radu's 30-yard effort on 36 minutes was cancelled out by Sergio Floccari to give bottom side Sassuolo hope of taking a point.
Miroslav Klose restored the lead soon after, only for Reja's men to give it up once more as Antonio Floro Flores levelled.
But Cannavaro's own goal gave Lazio the three points and they sit 10th, just five points behind fifth-placed Inter.
Reja, in his second stint as Lazio coach, said he had a clear understanding with his players.
"I remember in past years at Lazio we finished fourth and fifth, yet I was heavily criticised. This is part of the game," he said.
"I prefer the clear and honest rapport I have with everyone in the locker room."
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