Arsenal suffered a 3-2 defeat to Manchester United away from home at Old Trafford on Sunday afternoon.
Also on Sunday, Tottenham got the better of Swansea City 2-1 at White Hart Lane in North London in the league.
This means that Spurs are second in the Premier League table at the moment with 54 points from 27 matches.
Mauricio Pochettino’s side are two points behind leaders Leicester City and three ahead of North London rivals Arsenal, who are currently third in the standings.
Midfielder Dier, who can also play as a defender, is pleased with the defeat for the Gunners, but he has made it clear that he and his teammates are not concerned with other teams’ results.
"Arsenal losing is good news for us but we are working hard for us and not worrying about other teams,” the England international told BBC Sport (16:06).
There is still a long way to go this season, but Sunday’s results at Old Trafford and White Hart Lane could play a massive part in the title race.
Arsenal can certainly bounce back, but the way Spurs and Leicester are picking up points at the moment suggest that the Gunners are now third favourites for the league title.