Sarri's side trailed Atletico for most of the match after Pablo Barrios had broken the deadlock for the visitors in the 29th minute. However, a header from Provedel secured a vital point for the team.
"Trailing at half-time considering the way the two teams had played their football was not fair, and we risked feeling like victims of bad luck, of surrendering to the circumstances," Sarri told Sky Sport Italia.
"The team did not do that and received the correct reward."
Lazio have made a poor start to their domestic season, with one win and three defeats in their first four Serie A games, leaving them in 15th place. However, Sarri said things were looking up.
"People claim we are struggling, but in the last three games we have faced Napoli, Juventus and Atletico Madrid, ending up with a win, a defeat and a draw," he said.
"Atletico Madrid are very strong on the counter-attack, so there was every chance we would struggle, but we allowed them none except for the final 20 minutes when we were chasing the game."
Feyenoord top Group E after the Dutch side's 2-0 victory over Celtic on Tuesday.
"A point can be important for us, because we got it against the favourites of this group," Sarri concluded.
The 64-year-old Sarri admitted that he certainly hadn't expected Provedel to grab a last-gasp equaliser.
"We found a solution eventually!" he added with a smile.
Lazio's next Champions League clash will be at Celtic on October 4.
