Gaston Ramirez fired Saints 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.
"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."