Essien was penalised for blocking a shot with his arm and Sergio Aguero dispatched the resulting spot-kick to score the first of City's two goals in a 2-1 comeback win.
Chelsea manager Roberto Di Matteo, however, labelled the decision "harsh" on Essien, who he did not think could have got out of the way of the shot.
But Poll disagreed, pointing out that Essien's arms were extended in an attempt to make himself bigger and therefore block the shot.
"Michael Essien was only a couple of yards away from Pablo Zabaleta as the City player struck a fierce shot," Poll explained in his column for the Daily Mail.
"However, Essien had both arms above his head in an unnatural position. He was, as some might say, making himself as big as possible. So referee Dean was correct to award the penalty."
Chelsea are 7/1 with Bet365 to beat Tottenham 1-0 at Stamford Bridge on Saturday.
The 48-year-old added that Chelsea could not complain having taken advantage of a similar decision to continue their progress in the Champions League.
"While title rivals Manchester United might dispute the decision, Chelsea would find it difficult to, having benefited from a similar one awarded against Napoli last week," Poll said.
How do you stay up to date with football when on the move? With http://m.goal.com – your best source for mobile coverage of the beautiful game.