Jermain Defoe's first-half goal looked like settling it but Aleksandar Mitrovic's late header earned Newcastle a precious point in their fight to stay up.
"I couldn't show them I was really angry (at halftime) -- it was more about managing the situation," Benitez who was sacked by Real Madrid after just seven months in charge this year, told reporters.
"We weren't doing the best first half, we had some chances and they had some chances, and then we conceded at the end.
"I had to give them confidence and I had to give them an idea of how to play, how to deal with the situation in the second half, and I think that they did really well," added the Spaniard.
A draw did little for either side's survival prospects and left both of them below the trapdoor.
Newcastle are second from bottom, one place below Sunderland and three points behind 17th placed Norwich City.
"To get just one point, I'm not very happy, but the way that we got the point really pleased with the reaction of the players and the fans," Benitez added.
Benitez praised Mitrovic who has struggled in his first season in the Premier League.
"I said before that he has the potential," Benitez said.
"We have to help him a little bit with better crosses, better deliveries and support and get closer to him, but he will score goals if we can do that."
After the international break Newcastle face Norwich in a must-win game and Benitez believes the way the team responded against Sunderland will stand them in good stead.
"The way that we were playing the second half, was really pleasing, and hopefully we can keep this momentum for the next games," Benitez said.
"I think we can stay up. We have to keep working, I believe they can play better and from what I have seen today in the second half, they can do well."
(Reporting by Martyn Herman, editing by Alan Baldwin)
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