Chief executive Vinai Venkatesham, appointed in 2025, said Spurs required a "complete reset", adding that the club had drifted away from a "relentless obsession with football success".
Spurs only secured survival on the final day of the season with a 1-0 win over Everton, avoiding relegation by two points after a chaotic campaign involving three managers.
In an open letter to supporters, the Lewis family said they were "bitterly disappointed" and accepted responsibility for the decline, adding: "Finishing 17th this and last season does not reflect the stature or potential of this football club."
They admitted: "Football success had not been driving our decisions," but insisted Tottenham are "not for sale" and promised significant investment across the squad, academy and infrastructure.
The upheaval has followed the exit of long-serving chairman Daniel Levy after nearly 25 years in charge, marking a major shift in leadership.
Non-executive chairman Peter Charrington said the club had failed to build competitive squads, stating: "We did not build squads good enough to compete in the most demanding league in the world."
The season included a failed interim spell for Igor Tudor, who did not win a Premier League match in seven games before leaving after 44 days.
Tudor was appointed after Spurs failed to land Roberto De Zerbi mid-season, a decision Venkatesham admitted was a gamble, saying: "Was it a risk? Absolutely."
De Zerbi eventually arrived in March and helped stabilise the team, guiding Spurs to survival with a strong late-season run.
Venkatesham praised his impact, saying: "He has made an extraordinary impact so far."
He also warned that the squad needs major work, adding: "The squad needs work and the squad hasn't got the right balance."
De Zerbi has been backed as the central figure in the rebuild and signed a long-term contract, with the club believing his style matches supporter expectations.
The Lewis family reiterated their commitment, saying: "We are all in. We are investing in it. You will see more of this in the coming months."
The club now face a crucial summer after narrowly avoiding their first relegation since 1977, with leadership changes, recruitment plans and structural reform already underway.
Mikel Arteta's transformation of Arsenal was recognised on Tuesday after he was named Premier League Manager of the Season following the club's first league title triumph in 22 years.
Arsenal signed off their historic Premier League-winning campaign with a 2-1 victory over Crystal Palace at Selhurst Park, but the football quickly became secondary to the celebrations that followed.
Departing Manchester City manager Pep Guardiola said on Friday that the club should not look for a direct replacement in his image, warning that attempts to copy another coach's style rarely succeed.
Arsene Wenger told Arsenal players to "enjoy the moment while Ian Wright led emotional scenes outside the Emirates Stadium after Arsenal were crowned Premier League champions for the first time in 22 years on Tuesday night.
