The North Londoners finished second with 86 points, enough to win the title in 11 of the 24 previous Premier League seasons, and above their arch rivals Arsenal for the first time in 22 years.
They also continued their development under Mauricio Pochettino, building on their fifth and third place finishes in the Argentinian’s first two seasons at White Hart Lane.
But former Tottenham midfielder Freund says this gradual improvement means nothing if they cannot add to the trophy cabinet in the coming years.
“Tottenham had a great season, came close to winning the league and it’s so important to be playing in the Champions League,” said Freund.
“But Spurs have to go to the next stage now because Manchester United’s season was even better, because they won three trophies and they are in the Champions League too.
“Coming second is a great season but it’s time they win some silverware now.”
Former Germany international Freund, who also had a spell at Leicester City, believes Tottenham are not far away from winning silverware on a regular basis however.
Freund added: “They’re close and only need to take the last step.
“I think it’s a little bit experience, players like [Harry] Kane and [Dele] Alli will be better next season but they need some more confidence.
“They need players that can push them to be even better so if they’re fit they always play because they’re both unstoppable.”
The Lilywhites will play their home games at Wembley Stadium next season, while White Hart Lane undergoes construction work for Spurs’ move into their new ground.
Pochettino’s men struggled to replicate their form at the Lane when playing their home European matches at Wembley last season and have won just one of their last nine matches at the national stadium.
Freund does not expect them to have the same struggles throughout next season however, and is instead keen to stress the positives of the new era at the club.
“I think it’s an exciting time at Tottenham now, the new stadium is being built so everyone is looking forward to that,” said Freund.
“It may even be better than Wembley because it’ll be tighter and with 61,000 supporters really close to the pitch it could be the best stadium in the world.
“So I think all the players will be looking forward to an exciting season and I think they’ll finish in the top four once again, but the next step is to start winning some silverware.”