Saints salvaged a draw thanks to Virgil van Dijk’s equaliser deep into added time, after Jermain Defoe had given the Black Cats an 85th-minute lead.
Defoe’s strike came shortly after José Fonte had been dismissed for bringing down Fabio Borini when the Sunderland forward was clean through, and given the situation his side were in going into the final minutes, Koeman said he was willing to take a point.
He told Southampton’s official YouTube channel
: "If you tell me before the game you take one point out of today then I wasn't happy and I didn't agree, but after 90, 94 minutes yes, because 1-0 down, ten men on the pitch and that’s sometimes strange in football – maybe that last five, six minutes was the best football we showed today.
“We were struggling in the first 85 minutes. What I saw from the team, from the players individually, was not the level what they can bring.
“Maybe [there was] a lack of confidence and then it's difficult, because [Sunderland] played out of a good organisation, were physically strong, and you need extra quality and that wasn't there today.”
Koeman also felt Fonte was slightly unfortunate to have been sent off after the tangle with Borini in the 79th minute.
"It was a little bit unlucky,” he said. “I think it was really a fight for the ball and you know if it's a whistle from the referee that it's a red card, because José was the last man on the pitch.”