Wednesday’s second leg defeat against the Italian side came at Wembley, the club’s temporary home while a new 62,000-seater stadium is constructed on the site of their former White Hart Lane ground.
And Pochettino – whose team are scheduled to return to north-east London in the summer – believes a settled environment is vital to success.
“First of all to be in a place that you feel at home, in your new stadium, everything is stable,” the Argentinian replied when asked what is required to progress to the next level.
“That, I think, is the most important.
“This season, it’s Wembley and we feel very good, but all of the stress at the beginning, always we are going to pay for this.
“For our fans, for everyone, the process will start next season, start to feel like a home in the new stadium.
“That’s not an excuse, that is the reality and when we assess the team, we cannot put (leave) this out. We need to include this situation.
“We’re in a good way to create a massive club because we have all the tools to be one of the biggest clubs in Europe.”
Tottenham have little time to dwell on their European disappointment as they travel to Bournemouth on Sunday looking to boost their top-four aspirations in the Premier League.
“They feel strong against big teams like Chelsea, they are capable to win against Chelsea and Arsenal,” he added.
“They try to play football, (with a) philosophy like a big club.
“They try to dominate.
“Always against the big teams, they make very big performances.”
Spurs midfielder Eric Dier faces a late fitness test on an elbow injury ahead of the game at the Vitality Stadium, while defender Toby Alderweireld remains sidelined with a hamstring problem.
Full-back Serge Aurier returns to contention following his European suspension.
Former Manchester United captain Nemanja Vidic says he wants to become a “real manager” rather than just a modern-day coach.
The 36-year-old, who is in the middle of completing his coaching badges, says players these days have more power than managers,
But he said football has changed in the two years since he retired, and players now have “more power” than managers.
“I think the role of the manager has changed – he is becoming a coach,” the former Serbia defender said in an interview with the BBC.
“Players want the money and have more power – more power than the managers. It could frustrate me.
“When I was a player I don’t think I used my power. I didn’t think I was above the manager; I respected the manager. For me, it was coach, manager, CEO, owner.
“I don’t have experience to talk about players from a manager’s view, but the players definitely have the power now.”
“There are no more managers any more, just coaches now,” said Vidic, who played for eight years under Sir Alex Ferguson, arguably the last successful old-school manager given the recent travails of Arsenal manager Arsene Wenger. “I would like to be a real manager.”
“Alex Ferguson made it look easy,” he added. “You watched him and thought: ‘I would like to do that.’ But then I went to play in Italy. Then it didn’t look the same.
The Serbian says he would prefer being a manager to a pundit like his former colleagues in United’s back-line, Gary Neville, and Rio Ferdinand.
“I understand it is difficult – but I have played football all my life. For 28 years, I had about 15 managers. It’s what I know.”
“I am used to the stress. Winning, losing, happy, sad. You want to win again. You want to prove something. You want to make the difficult decisions and test yourself.”
The Red Devils are currently second in the league and 16 points behind champions-elect Man City, but Jose Mourinho’s men are in the last-16 of the Champions League.
And Vidic, who was the last United skipper to lift the league trophy in 2013, told the BBC that United are equipped to succeed in Europe.
“When the season started, I thought United had more chance to win the Champions League than the Premier League because the players they signed didn’t have the time to fit in.”
Vidic believes that in Mourinho, United have a manager who understands the path to European glory.
“Mourinho is a tactical coach and knows Europe very well. He knows there are going to be scrappy games and how to get through them,” he said.
“To win, you need a bit of luck – but there is a chance to get to the semi-finals or final. You never know. And if you win a Champions League, the players start to believe.
“Phil Jones, Chris Smalling, they will look different to now. It is about the perception of the people – you have to win.
“Players then believe more in themselves. They start to perform better.”