Pep Guardiola hailed his Manchester City players as 'amazing' despite them missing two penalties and dropping points against Everton.
De Bruyne and Aguero - who started the game on the bench - were the culprits from the spot and Everton made the most of their goalkeeper's brilliance by taking the lead through Romelu Lukaku (64).
Nolito equalised (72) within a minute of coming off the bench before Stekelenburg pushed a stunning late De Bruyne effort onto the post as Guardiola lost his 100 per cent home record as City manager.
City are now two games without a win after losing to Tottenham in their previous game, but Guardiola refused to criticise his team, who remain top of the Premier League but only on goal difference ahead of Arsenal.
"We did everything," Guardiola.
"I'm so proud of my team. We played amazing, but we didn't win. We missed penalties and created chances. They had one chance and scored. But that's football.
"Football is the only game where you can do everything and the opponent has one shot on target and you lose the game. Tennis and basketball is not like this. We did absolutely everything."
Former Barcelona team-mates Guardiola and Everton boss Ronald Koeman locked horns as managers for the first time.
The pair won four La Liga titles and one European Cup during their five-year spell together at the Catalan giants.
Guardiola praised the way Koeman organised his troops in defence.
"I'd like to compliment Everton as they defended very well," he said.
"I'm sad for my players as they deserved to win today. We will improve on that. We keep our heads up and have no regrets about our performance.
"Every game, whether you win or lose, you learn. I am new here and I'm still getting to know my players."