A Luke Young piledriver cancelled out Darren Bent's opener for Spurs and Southgate said: "I don't think we should have won. I think from being a goal down at half-time, we have got to be pleased with the result.
"Obviously we are in a spell where lots of things are going against us but we just have to dig in. It wasn't the ideal way to come in at half-time. I don't think there was much in the game before the goal.
"Then we tried to equalise straight away and there was a five-minute spell where we looked a bit ragged.
"Credit to the lads, at start of the second half I thought we created enough pressure and put Tottenham on the back foot, culminating in the goal which was a fantastic strike from Young.
"Then, unfortunately, we lost a bit of momentum because we ran out of fresh legs to put on.
"We know that we are going to get criticised because people will read it as an opportunity for us to get three points but I think everybody knows that Tottenham are in a false position with the players they've got.
"I don't think they'll stay there so it was by no means a banker for us. We have got a point out of it which pleases me and it gives us something to build on. We had to stop the run we were on."