Tottenham's Christian Eriksen and Oliver Skipp both missed penalties in the shootout, with the latter unlucky not to convert his after a brilliant save from Samir Handanovic for Inter Milan.
Romanian prospect George Puscas had his penalty saved by Paulo Gazzaniga, who has impressed in his last few penalty shootouts for Spurs.
Lucas Moura scored in the opening stages for Spurs with a powerful strike, but Inter hit back through a goal from Stefano Sensi after a brilliant one-two with 17-year-old Sebastiano Esposito.
Calls to sell Eriksen from fans
Christian Eriksen's second poor penalty in a week accompanied with his work ethic and body language gave many Spurs fans and neutral viewers the impression he did not want to be at White Hart Lane.
The Danish attacking midfielder looked sluggish and tired which is uncharacteristic for him - having topped most games last season for most kilometres run in the 90 minutes.
The 27-year-old has been linked with Real Madrid all summer, but according to reports, the only viable option for Eriksen this transfer window, if he was to leave, would be to Atletico Madrid.
Ndombele needs time to settle
The Lilywhites' new record signing Tanguy Ndombele may take longer to settle in at the North London club than just the length of pre-season.
Speaking to reporters after the game, Spurs boss Mauricio Pochettino reminded everyone it will take time to see Ndombele at his best.
"For him it’s difficult. We cannot expect too much," said Pochettino.
"We need to accept he needs time to adapt to first a new culture, a new country, new habits.
"Of course it’s only him who arrived to the club and that makes it more difficult. When a few players are new they can help each other but it’s only him.
"We need to give him time but I am happy in the way he is adapting. He is open to improving and learning but needs time to (until we) see the best version of him."
Pochettino open to signing more players despite Daniel Levy being in Miami
Pochettino was clearly frustrated after the Audi Cup game against Real Madrid with his position at the club, amid reports earlier in the year that if the club did not strengthen where the Argentine wanted, he would be open to managing another team.
With less than four days of the transfer window left, Tottenham may be gearing up for a hectic transfer deadline day.
"(Daniel Levy) is in Miami and I have not had the chance to speak with him," said Pochettino.
"I am happy with my squad. You can see today a lot of younger players.
"In every season we are always open to improve the squad and to try to find the right players to be stronger and better and there are still four days.
"We'll see what happens in the next few days."
Where to watch Tottenham's first game of the new season
Tottenham kick off their Premier League campaign against newly-promoted Aston Villa on Saturday 10th August at 5:30PM (BST) and it will be live on Sky Sports Premier League.