The Lilywhites have finished third and second in the last two Premier League seasons under Mauricio Pochettino, picking up more points combined during those campaigns than any other team in the division.
Spurs remain without a trophy since 2008, however, and Dier insists that his side cannot be truly pleased with their efforts in recent years unless they end that decade-long wait for a major honour later this season.
"I think we should be proud of what we've managed to do so far, but I don't think we can be proud of achieving anything because I don't think we have. We can be proud of where we are now, considering where we've come from," he told Sky Sports News. "I think we can definitely be proud of that.
"But as a group, I think we wouldn't be happy unless we won something. The manager is very ambitious, and we've created a fantastic working environment where everyone is really hungry for success. That just came out on the pitch.
"I think the feeling within the place was positive, we felt things were going in the right direction, and hopefully they will continue to, because we might have challenged a couple of times but we haven't really done anything yet."
Dier, who has been at Spurs since joining from Sporting Lisbon in 2014, is expected to play a part in Saturday lunchtime's London derby meeting with West Ham United.