The reigning champions were edging towards a much-needed run following a run of disappointing results in the Premier League.
However, Palace were awarded a penalty in second-half stoppage-time and Michael Olise scored from the spot to make it 2-2.
Guardiola was visibly enraged in the aftermath and cut a highly animated figure on the touchline as City dropped points once again.
Hodgson would have been delighted with his side's result and couldn't help but notice his counterpart.
Cameras from the game saw Guardiola angry on the touchline, with the Palace boss just looking over and smiling at him.
MORE ON THE PREMIER LEAGUE
Lockyer stable and responsive after suffering cardiac arrest as Luton match abandoned
Man City suffer title blow as Palace stage comeback to delight Arsenal and Liverpool fans
Speaking after the game, the Man City boss made no excuses, saying: Guardiola said: "It's not bad luck, it's deserved. We gave away two points. When you give away this penalty, you deserve it.
"You see the chances we created and conceded it's quite similar to all this season apart from the game - but we are not able to close the games. That is the feeling.
"At the end, be patient and don't concede transitions and don't concede like we have done in seven or eight years in these type of games.
"But of course in the first action they run and score a goal and in the last minute we give them [a penalty]. In the 18-yard box you have to be careful and we weren't. We don't deserve to win."
Most read in Football
Lockyer stable and responsive after suffering cardiac arrest as Luton match abandoned
Newcastle's nightmare injury crisis gets worse as two stars limp off against Fulham
Fan emergency halts women's north London derby before Spurs make history against Arsenal
David Wagner calls for 'idiot' Ipswich fans to be banned after Delia Smith car incident
City have now won just one of their last six matches in the Premier League, with the latest result affecting their title challenge.
Jack Grealish and Rico Lewis gave them a 2-0 lead but Palace fought back through Jean-Philippe Mateta and Olise.