The Blues had 32 per cent of possession and scored with both their shots on target, as wing-back Marcos Alonso opened the scoring with a delightful free-kick before cancelling out Michy Batshuayi's own goal with an 88th-minute winner.
Antonio Conte set up his team in a 3-5-1-1 formation that included David Luiz in midfield alongside N'Golo Kante and new signing Tiemoue Bakayoko, with Cesc Fabregas and Gary Cahill unavailable through suspension and Eden Hazard still absent with injury.
Despite struggling to break the Blues down, Pochettino claimed his Spurs were superior to their opponents and were unlucky to not get a result.
He also dismissed claims the club was struggling to adapt to their new Wembley home while White Hart Lane is being redeveloped.
"We were much better than Chelsea," Pochettino told a post-match news conference. "It was very clear their idea: to try and contain us and play on the counter, with Morata and Willian in front."
"I am very happy. I think we were a little bit unlucky. If you have sometimes this percentage of luck, it can be difficult to win."
The Argentine tactician stopped short of declaring Chelsea's tactics as not befitting of a defending champion, stating he wasn't criticising their overall style.
"I am only explaining the game today. I'm not saying they are a defensive team. They played differently only today, not the normal way," he said.
"It's true they tried to defend deeper and go on the counter-attack with Morata and Willian. But I am so pleased with our performance."