The Saints were on course for victory 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.
"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."
He added: "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."
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."
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- Andy Carroll