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Spurs qualified for the Champions League for a third consecutive season thanks to Harry Kane's winner in a nervy 1-0 win over Newcastle allied to Chelsea's 1-1 draw at home to Huddersfield.
Victory also moved Pochettino's men above Liverpool into third, and he believes their success this season is even more laudable having played the whole campaign at a temporary home in Wembley.
"For the club (it) is a massive thing to move to the new stadium and play Champions League," said Pochettino.
"It will be another massive challenge because it will be the same as playing in Wembley. It will be a fantastic stadium, but you need to make the stadium your home."
Despite undoubted progress in Pochettino's four years in charge, Spurs have still yet to win a trophy under the Argentine.
And he accepted that silverware is the next challenge having established Tottenham as a regular in the top four.
"The first step is to be competitive, to reduce the gap with the top four, and that was the challenge four years ago. Now it is the first time in 23 years in the Premier League Tottenham is above (all) the (other) London clubs.
"Next is the trophy, but you need to build. We are not in a club that won a lot in the past years."
Spurs had won just one of their previous five games as a late season slump threatened to cost them Champions League football.
And in their penultimate match at their temporary home, the hosts were grateful to some good fortune and wayward Newcastle finishing to seal their return to Europe's premier club competition next season.
Jonjo Shelvey smashed a free-kick from the edge of the box off the post before Hugo Lloris produced a fine flying save to his right to parry a powerful header from Jamaal Lascelles.
Dwight Gayle headed over a decent opportunity with a free header from close range and then saw a tame effort comfortably handled by Lloris once more.
With tension among the home support rising, Spurs fans could barely believe their eyes when Kane completely failed to make contact as the ball fell invitingly for him with just Dubravka to beat just before the break.
Kane hasn't been at his best since returning from ankle ligament damage last month that kept him sidelined for three weeks.
However, England's talisman still can't be offered too many clear-cut chances, and he made amends to settle Spurs' nerves five minutes into the second-half.
Son Heung-min's low cross teed up Kane to open his body and curl home his 39th goal of the season into the top corner.
There were still a few scares to survive for Spurs as Ayoze Perez fluffed his lines with a great chance to equalise and substitute Jacob Murphy then had the visitors' best chance of the night, but blasted high and wide to a palpable sense of relief.
The Spurs fans rose to their feet to greet Toby Alderweireld's return as a substitute. The Belgian has been sidelined by Pochettino in recent months reportedly due to his refusal to sign a new contract with the club.
And seconds later there were more celebrations as news of the full-time score filtered through from Stamford Bridge that Chelsea's Champions League chase had faltered
