Asked about his side's performance against Paolo Di Canio's men, Pochettino reflected on the possibility of points dropped.
"I think it's clear that we did not deserve to lose today," he said. "When we review the match later on we'll probably feel we deserved all three points."
Pochettino aired his frustrations at Sunderland's opening goal, when Emanuele Giaccherini found himself unmarked in the six-yard box to head home.
He added: "I fully take responsibility in that sense. It just shows that we have to improve. It's not acceptable that we step onto the pitch in that manner. We were basically asleep.
"It's a big lesson for us. It'll help us to improve."
However, the Saints manager seemed happy with his side's overall play.
"We had the best chances, and we actually deserved the three points. We just have to look ahead and prepare well for the coming games.
"I would prefer to have six (points) at this moment. But we have to grow and we have to learn. The league is in full swing now."