Misses in the shootout from Jadon Sancho and Jonny Evans cost United, who were minutes away from victory when Alejandro Garnacho gave them a 1-0 lead eight minutes from time.
But after City held their nerve in the shootout having made it that far thanks to Bernardo Silva's equalising header in the 89th minute, Ten Hag wants defeat to mean something down the line as United open the Premier League season against Fulham on Friday night.
'We are disappointed,' he said. 'We have to feel the pain and everyone feels the pain, that's a good signal but also I see some positives.
'We performed well, we could've won this game, we were twice leading in the game and in the penalties, but we lost and we're disappointed. But we take the positives.'
Marcus Rashford, who struggled last season and finished with only eight goals having bagged 30 goals in Ten Hag's first season at United, missed two golden opportunities in regular time, but his manager is not concerned about his confidence.
'No. No. I think he was several times in very good positions,' he added.
'I'm very pleased he is getting in those positions, because I know with Rasmus [Hojlund], keep going, keep making those movements and the team will make those movements, he will score goals.
For victorious manager Pep Guardiola, who took to the Wembley touchline in a very casual t-shirt and jeans combo, he is not as convinced as supporters that this win proves his side's hunger to win a fifth Premier League title in a row.
'I would like to answer yes but I don't know,' Guardiola said.
'Not for the fact that we scored with a minute left at the end of the game. Arsenal did it last season and won on penalties, last season we lost.
Marcus Rashford missed two golden opportunities in regular time, but his manager is not concerned about his confidence
'We could have lost today, we were close to losing with minutes left so we have to wait.
'We are far from our best. It's normal but it's better starting with one trophy won.