Spurs' top-four exploits should not be taken lightly but the constant clamour for trophies means they cannot rest on their laurels.
Pochettino is happy with what they have achieved this season, with an impressive league campaign backed up with a run to the last 16 of the Champions League and the FA Cup semi-finals.
"You cannot finish with the feeling that it was not enough," he said. "A lot of amazing things happened.
"To beat Real Madrid, to finish top of our Champions League group, when it was Dortmund, Madrid, amazing victories at Wembley against Madrid, Liverpool, Manchester United, nearly all the teams.
"After 28 years, to win at Stamford Bridge. Many amazing things happen.
"But sometimes, I don't understand the negativity. If you want to win, you need to arrive to the semi-final and final.
"To arrive there, to be competitive, that is a step you cannot jump. And of course in the next few years the challenge now is to win some titles.
"But it was also a challenge for us to be consistent, to put the team in the top four, and in four years we are going to play three times in the Champions League. That was the target."