Harry Kane's double earned Spurs a third win in four matches and maintained their impressive start to the campaign in another game where Antonio Conte's side were forced on to the back foot for long periods.
"I think obviously since the manager arrived we've improved in many aspects, I think the mentality is one," Dier said.
"We did well in that sense in this game [at Forest]. Difficult moments, I think right at the start of the game defending set plays, at the end the same. In those moments, staying strong together.
“And yeah I think we're happy to be picking up the points we're picking up. I think we can play a lot better but it's good we're still managing to pick up the points. Maybe that's where the mentality comes in. I think we can play a lot better than we have been in these last couple of games.
"We're happy to have the points that we do. We've done well to get them, shown a lot of different qualities to get them but we can perform a lot better than we have been. I think that's what is exciting as well.
"Tough game, tough place to come," Dier added. "Great atmosphere, great experience to play here in this atmosphere. We're happy to have won.
"We took our chances, we defended well as a team, kept a clean sheet. And we know if we keep a clean sheet we'll definitely create chances and score goals."
Kane's double either side of half-time moved him on to 201 career goals and ahead of Andrew Cole to third on the list of all-time Premier League top scorers.
The striker also missed a penalty -- his first failure in 22 attempts -- when Dean Henderson pulled off a smart save, but Dier is confident he will score the 74 more goals needed to surpass Alan Shearer's Premier League record of 260.
"Obviously if he gets his chances he normally scores them," Dier said. "The penalty is a rarity and obviously he's so effective in front of goal. I'm pretty sure he'll end up in that No.1 spot."
Kane's second goal was made brilliantly by substitute Richarlison, who hunted down possession on the left touchline and crossed with the outside of his boot for the England captain to head home.
"I think we're always going to create chances and we did that. We could have scored a few more," Dier added.
"We have great options. Richy was fantastic when he came on, the energy he gave us and a fantastic cross for the second goal as well. He's going to be a really really important player for us I'm sure."