Saints beat the east Londoners to automatic promotion from the npower Championship last season and were on course to get another one over them when Gaston Ramirez fired them ahead in the second half.
That lead lasted just seven minutes, though, as Andy Carroll struck home via a slight deflection off Steven Davis to earn a share of the spoils.
The 1-1 draw leaves both sides in mid-table and seven points clear of the drop zone, meaning Premier League survival is all but secure.
"I am happy with a point in the end," visiting boss Allardyce said. "I thought we were more than comfortable.
"Our away goals have been our big problem all season and I think the chances we created today, it looked like we wouldn't score again.
"We had some really good chances that we didn't convert and then they went 1-0 up through a pretty lucky goal.
"But it was a really good comeback, Andy has got another goal for us so in the end a point is very satisfying when you have gone a goal down and haven't scored as many away from home as we have.
"I think that was only our 10th goal away from home. It has brought us a point and one nearer to the magic 40.
"We have six games to go, with four at home and two away, so we will see where we will finish.
"I find it highly unlikely that we won't pick up any more points up. You never know in this game but I can't see us losing six on the trot, especially with the determination of the lads and the way they have been playing.
"Having beaten Stoke, we've got a win, two draws and only one defeat. You have to fancy us to pick up some points from here on in.
"We have Manchester United on Wednesday and then Wigan on Saturday so it is a big week for us, starting with a very precious point here."
Saints boss Pochettino cut a slightly more frustrated figure than Allardyce, although was pleased by his side's performance in wet and windy conditions.
"We had a feeling we could win the game, but were not able to," the Argentinian said. "We put in a big effort to get the three points and conceded very quickly after we scored.
"It was hard to play on a pitch that was so wet against an opponent that are physically very strong, so overall I think we did a very good job against them.
"I congratulate my players because they did quite well in conditions that actually favoured the rivals' style of play.
"Even though the conditions favoured them, we actually played well.
"I think we played the game as we wanted and should have. We imposed our brand of football.
"I think we defended well, nullified their style of play and cancelled them out.
"It is just a shame about the result because our performance was really good."
Southampton lacked the verve displayed in recent weeks, although that could be due to the virus that hit the squad this week and saw the in-form Jay Rodriguez and Luke Shaw dropped out the starting line-up as a result, with the latter missing out on the squad altogether.
"I don't know the virus personally but I know there have been four or five players affected by the virus," Pochettino said.
"We haven't been able to train properly throughout the week because of it.
"It was a risk to bring Rodriguez on as he was only able to train yesterday [Friday]. The energy he displayed in the 20 minutes he was on said a lot about him but overall it was a bit of a risk."