The Giallorossi were looking for a response after a 0-0 league draw with relegation battlers Genoa and 2-0 Coppa Italia defeat by Inter Milan in the last week.
"If you had asked me at the start, I would not have wanted a draw, but in the 90th minute, definitely," Mourinho told DAZN.
"It isn't the result we wanted, but if nothing else we haven't lost in the last four in Serie A, we have got eight points."
A Tammy Abraham penalty gave the capital club the lead at the end of the first half, but a mistake from goalkeeper Rui Patricio led to a Chris Smalling own goal for the equaliser, before Hamed Traore completed the turnaround with a well-taken strike.
However, Sassuolo defender Gian Marco Ferrari picked up a second yellow card with 12 minutes remaining and Roma capitalised deep in stoppage time through a Cristante header.
Elsewhere, bottom two Genoa and Salernitana played out a 1-1 draw that did little to help either sides' hopes of survival, leaving them six and nine points adrift of the safety zone respectively.