Goals from Jay Rodriguez and Dejan Lovren put the visitors in charge at the Stadium of Light, but Poyet was able to witness an impressive comeback from his side.
Fabio Borini halved Sunderland's arrears immediately after Lovren's volley, before Adam Johnson's fourth goal in two matches rescued a point for the Premier League strugglers.
The winger was shown on to his right foot by the Southampton defence and lashed an effort into the top corner with 19 minutes remaining.
"It was looking really bad," Poyet admitted. "We couldn't make a pass together, couldn't cope with the pace, power and passing game of Southampton.
"It was looking dark but the (Borini) goal came at the right time.
"We need to be realistic; this is a point gained because we were far from being good enough in the first half. It is incredible how much we changed in the second half.
"The second half is the best part of our game. We have been working on things. The subs have been outstanding. If they keep believing maybe it is going to be possible (to avoid relegation)."
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.