Pochettino conceded defeat in the race for top spot, following Spurs’ failure to beat West Bromwich Albion at the weekend.
Tottenham could only pick up a 1-1 draw at Wembley, which leaves them 13 points behind league leaders Manchester City.
Pochettino has already admitted that the gap to City has now become unassailable for Spurs, even at this early stage of the campaign.
But Dier was not prepared to concede defeat so easily, and insisted that nothing would be decided until January.
“There’s so far to go,” he said. “We’re starting to get into the really busy period around Christmas, which is really key. If we want any chance we have to have a great festive period. I think only after the festive period, maybe at the end of January, that’s where you have a clearer idea of where everyone is.
“In the seasons I’ve been here we’ve had really strong festive periods and that’s where we’ve caught up a lot of teams and put pressure on teams. We’ve just got to focus on ourselves and try to have a really good run of games now.
“It’s the Premier League. It’s the most exciting league in the world for a reason. Every season it goes down to the last couple of games and I don’t think this season will be any different.”
Tottenham’s struggles to win at Wembley has been their major problem so far this season, with the Lilywhites dropping points far too regularly in front of their own supporters.
Spurs have now slipped down to fifth place in the Premier League table, after what has been a poor run of form in domestic matches.
Tottenham are next in action tomorrow evening, when they take on Leicester City at the King Power Stadium.