City would have gone fifth and above Newcastle with a victory, but instead remain sixth and 12 points behind leaders Liverpool, who drew 1-1 at Nottingham Forest.
Brentford move up a spot into 10th, above Brighton on goal difference.
Even after Brentford had got a goal back, City had chances to restore their two-goal advantage but Savinho and Erling Haaland had attempts saved while James McAtee, who scored a hat-trick against Salford, fired just wide.
Guardiola's squad did not include England defender Kyle Walker, after the 34-year-old earlier this week said he was looking to leave the club in the January transfer window.
Brentford made a bright start as Wissa shot wide, had a shout for penalty rejected and narrowly missed Mbeumo's cross.
Ortega, preferred in goal with Ederson only on the bench, made a smart save low down to his left to keep out an effort from Mbeumo and also did well to deny Vitaly Janelt.
But City grew into the game with Savinho hitting the post early in the second half and he fired another chance into the side netting before Foden's double had City on course for the win, only for Brentford to produce an inspired fightback.
"The whole performance, I'm extremely happy with that," said Brentford boss Thomas Frank.
"We went toe-for-toe with one of the best teams in the world who can produce unbelievable pieces of brilliance. It was a well-deserved point. We lacked cutting edge before the goal but we showed that in the last 10, where we showed a fantastic mentality."
The Bees entertain Liverpool on Saturday, before City will be looking to return to winning ways at relegation-threatened Ipswich Town on Sunday.