Our 11-game winning streak was brought to a halt by the London side in a thrilling game at the Etihad Stadium.
Rodrigo rescued a point with a late equaliser after Raheem Sterling gave Chelsea a first half lead but the Portuguese says the players were unhappy with the first-half performance.
“We’re not satisfied,” he said. “We’re disappointed. At home, we want the three points, always.
“The rhythm was not right and the patience with the ball. We needed to put more pressure on Chelsea - that’s what the first half lacked - it wasn’t good enough for our standards.”
While it was an entertaining game with 40 shots in total – 31 for City, Bernardo says that we lacked our usual control and rhythm that has proved so successful.
“We needed to play our game which is not a game of transitions, it’s a game of controlling the rhythms of the game,” he added.
“We know that if you play in a game of transitions - any team with quality - it’s 50/50 and we don’t want that. We let it happen.
“Credit to Chelsea. We needed more intensity in the high pressing and the duels.
“If you’re not at your highest level against teams like Chelsea, it’s not good enough. They caused us big problems in the transitions - we didn’t control it.”
City have a quick opportunity to put it right with Brentford visiting the Etihad on Tuesday night for the 19:30 (UK) kick-off.
Victory would move Pep Guardiola’s side into second place, a point behind leaders Liverpool, and Bernardo is expecting an improvement.
“[We need] a reaction, three points and back on track to try and get as many points as possible,” he said.
“We keep going and keep fighting but it’s a setback.”