The Sunderland boss accepts his side will now struggle to overhaul Swansea in 16th, with the Wearsiders trailing the Welshmen by eight points.
Jermain Defoe thought his 14th goal of the season had sealed a vital win at Southampton on Saturday, only for Virgil Van Dijk to grab a draw in injury-time.
Sunderland face relegation rivals and local foes Newcastle next on Sunday, March 20, but Allardyce has warned his men not to let Tyne-Wear derby fever detract from their survival fight.
“It’s not about Newcastle, or anyone else,” said Allardyce. “It’s about us getting to 38 points as quickly as we can.
“We should have had 27 now, we should have only needed another 11 from nine games and we don’t have that opportunity.
“The gap between us and the teams above us has got to a stage where we’d have to win three games on the trot and they’d have to lose three games on the trot, just for us to catch them.“
Jose Fonte’s red card 10 minutes from time opened up what had been a previously insipid encounter on the south coast.
Second-half substitute Defoe capitalised to prod home six minutes from time, before Van Dijk turned in Dusan Tadic’s cutback to snatch a point for Saints
Republic of Ireland striker Shane Long could be fit for Saints’ trip to Stoke next Saturday, but Charlie Austin is expected to miss several weeks with hamstring trouble.
Forster, Martina, Fonte, van Dijk, Bertrand, Romeu, Clasie (Juanmi 65), Steven Davis (Ward-Prowse 65), Mane (Yoshida 83), Tadic, Pelle.
Cedric, Reed, Stekelenburg, Olomola.
Mannone, Yedlin, Kone, Kaboul, Van Aanholt, Kirchhoff (O’Shea 90), Borini, M’Vila, Rodwell, Khazri (Larsson 76), N’Doye (Defoe 59).
Jones, Pickford, Toivonen, Mandron.