Spurs benefited from a dubious penalty decision as they won 2-1 at the Etihad Stadium in a highly-charged Barclays Premier League contest.
Harry Kane opened the scoring from spot after Raheem Sterling was harshly adjudged to have handled the ball as he turned his back to block a cross from Danny Rose.
It was the second time this season Clattenburg had frustrated City in a Spurs clash after two controversial offside decisions in the 4-1 loss at White Hart Lane in September.
Pellegrini said at his post-match press conference: "More important than my view of penalty is that everyone saw what happened
Unfortunately for us it was the same referee, Clattenburg, as when we lost against Tottenham in the first round with two clear goals offside.
"It was a penalty that was decisive for the game. I don't have nothing more to say."
Asked why he approached the fourth official after the game, Pellegrini said: "Just to congratulate the referee - about the decision."
When asked about the appointment of Clattenburg, Pellegrini said: "For me I don't think it is a good decision to have the same referee but I don't want to talk any more about that."
Pellegrini was pressed further on the matter but would not comment.
The Chilean said firmly: "I am finished with the referee."
City recovered after conceding the penalty to level through substitute Kelechi Iheanacho but Spurs snatched victory with an 83rd-minute winner from Christian Eriksen.
Pellegrini said: "I don't want to just talk about the decisions. It was a very close game, a very good game. We made a mistake for the second goal.
"But that moment, when the referee whistled for a penalty, was a very important moment, we were playing well."
The result lifted Spurs within two points of leaders Leicester and left City fourth, still six points off the top in a compelling title race.
It was a second successive damaging defeat after last week's loss to Leicester but Pellegrini insisted his team can still recover.
He said: "The last two results we had here at home were very bad. We never expected not to win a very important six points but we must continue fighting.
"I saw a very good reaction from the team. We have 36 points more to play for. It is very important to start working again and believe all things can happen."
Source: PA