Peretz, 25, noted that Saints knew they probably had to beat the Robins to remain in strong contention for the automatic promotion places.
The draw leaves them three points adrift of second place with just two league games to play, meaning play-offs are the more likely route.
But with a trip to Wembley up next, Saints cannot afford to dwell on the result and remain fully confident about their promotion chances.
“It’s frustrating because we came into this game with the knowledge that we had to win to go into the automatic places,” Peretz told the Daily Echo.
Southampton’s Daniel Peretz during the Championship match between Southampton and Bristol City at St Mary’s Stadium. (Image: Stuart Martin)
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“It didn’t happen, we can’t win every game. We want to, and will do everything for that, but it’s the reality now; we can’t change it.
“We must face up and look forward because we have a big game on Saturday. We are not thinking about [automatic promotion] too much.
“We just come into every single game with the fact that we want to win. If the situation happens where we go automatic, it will be fantastic.
“If not, ok, let’s go for the play-offs at the end of the season. We have a lot of confidence in ourselves and how we play after those runs.