After keeping it goalless until half-time, Spurs were blown away 3-0 in the second stanza.
And Dier admits his team were not savvy enough against their London rivals.
"To concede two goals back-to-back so quickly is difficult," Dier said. "We just needed to be a bit smarter in that moment when we conceded the first.
"Maybe come together more, stay in the game for five minutes and try to get back on the front foot. We were a little erratic in that moment. We conceded chances and then we were very unfortunate with the second goal. We saw almost an identical one in the Man United [versus West Ham] game earlier and there's nothing you can do about it. Hugo had no chance.
"It really was a game of two halves. We played very well in the first half and we have to focus on that, take the positives from that and build on it. Second half, they were the better team. We conceded the first goal very early in the second half and then lacked a bit of control to stay in the game and not concede the second.
"[We needed to] try to build and get back to the way were playing. But we conceded again and it became very difficult. We lacked that [control] a little bit but they were sloppy goals, all three of them. We can do so much better."
Dier added: "I think the important thing is that we were under no illusions after the first three games that we had a lot to work on.
"And we're the same now. We didn't get too carried away with those results and we shouldn't get too down now with these last two results. We know we have a lot to work on but I think we're going in the right direction. There was a great 45 minutes and now we need to find the consistency where we can do that for 90."