The defending champions were on top for long periods, with Aleksandar Kolarov and Sergio Aguero hitting the post either side of half time.
Following the latter chance, Kieran Richardson had the opportunity to open the scoring on the end of a lightning Villa counter-attack, only to be denied by a combination of Pablo Zabaleta and Joe Hart.
The hosts played a full part in an absorbing Villa Park contest but were left crestfallen when Yaya Toure stroked home his first goal of the season in the 82nd minute before Aguero rubbed salt in the wound two minutes from time.
"I think for 82 minutes of that game we were in it," said Lambert afterwards.
"Kieran [Richardson] had a really good chance - I know Aguero hit the post at the other end, that's how tight it is.
"Against these sort of teams, if you get a chance you've got to try and take it.
"We had one or two little chances but they're a right good side as well. In my own opinion they'll be first or second in the league.
"They're that good a side that they're always going to have chances against you. The defending, for 82 minutes the lads were excellent.
"The two lads that scored the goals are top players."
Villa sit a creditable seventh in the table following a gruelling run of fixtures, with Saturday's outing following a win at Liverpool and defeats against Arsenal and Chelsea.
Lambert expects a title tussle between Chelsea and Manuel Pellegrini's team, but he struggles to split the sides having seen them both at close quarters over consecutive weekends.
He added: "It's a close one. They're two really good sides. I think it's going to be a close one this year, that's for sure."
