Spurs, who have flattered to deceive in recent seasons, kicked off their campaign in uninspiring form but are now well-placed in fourth after 23 games.
They have high hopes of securing a top four finish for the first time since 2012 when they finished fourth but still missed out on the Champions League to Chelsea, who finished sixth, because they won the competition.
"There was pressure from the beginning of the season and obviously with us being up there and fighting for everything there will be added pressure, but we're all enjoying ourselves at the moment," Dier told the club's website.
"I don't think we play with pressure, we enjoy ourselves and we play freely. We're a young team, we express ourselves and hopefully we'll continue to do that."
Mauricio Pochettino's side, who play at Norwich later on Tuesday, have lost only three league games this campaign, with only leaders Leicester City (two) having lost fewer.
"We've had a couple of slip-ups like Newcastle and Leicester at home but in a way those losses have helped us because we've responded and gone on good runs," England international Dier said.