City, transformed by the introductions of Foden and fit-again Kevin De Bruyne, dominated the second half but were unable to add to their solitary goal.
Hammers keeper Lukasz Fabianski saved from Raheem Sterling and Riyad Mahrez at the death, to leave City with just eight points from their opening five matches.
They also lost Sergio Aguero to a probable hamstring muscle problem at half-time.
Injuries and have taken their toll on City, so much so that Guardiola named an unchanged starting line-up for the first time since October 2017, some 172 games ago.
Guardiola said: “We started really well, then after we conceded with the first action they had, we struggled in the last five or 10 minutes of the first half.
“In the second half we were better, we scored and had the chances at the end but we could not convert them, so we drew.
“I would prefer to have results but we have to analyse where we are. Many injuries, a lack of preparation, no recovery time, and tough games we’ve played so far.
“But the players gave everything on the pitch. Now we recover and think about the next game.”
The Hammers will be encouraged by another point, following on from Sunday’s dramatic comeback at Tottenham, and given that their record in this fixture is atrocious.
Antonio’s 18th-minute strike, hooking Vladimir Coufal’s cross over his shoulder despite the attentions of five defenders, was only the second goal West Ham had managed in six fixtures against the same opponents at the London Stadium – City had racked up 22 over the previous five.
Foden hauled the visitors level when he turned and poked home a low cross from Joao Cancelo.
Nevertheless eight points from West Ham’s tough opening run of six games is more than satisfactory for manager David Moyes.
“It was strange, I actually think we can play much better but I’m really pleased with a point,” said Moyes.
“We did some good things, more in the first half, the second half was very difficult. But it was brilliant character from the players again.
“It was different to Tottenham last week because they had to try and hang on and keep something, and they did.
“We’re improving as a team, our football is getting better and I’m really pleased with the way things are going.”
