City will go top of the Premier League if they avoid defeat against Swansea at the Liberty Stadium, in today's early kick off - live on Sky Sports.
Pellegrini's side are a point behind leaders Arsenal who play Cardiff later in the afternoon.
"I think it was a fantastic month for us," said the Chilean. "We played nine games in December, we won eight and drew just one.
"In the Premier League, from the last seven we won six.
"It was very important for us to recover points. Arsenal were six points ahead of us so it is very important to finish the year in the position we wanted to be.
"To recover six points in a month is not easy.
"We continue in Capital One and Champions League so I think the first six months of the year were very good for us. Now in the second half we try to win."
City were forced to work hard for a 1-0 home win over Crystal Palace at the weekend and Pellegrini believes his players will need another disciplined display against Swansea on New Year's day.
"Every team in the Premier League can cause problems to our team and to all other teams. That is why it is so close, this Premier League," said Pellegrini.
"I repeat what I have said, six or seven teams will be fighting for the Premier League until the end.
"We will continue exactly the same as in the first half.
"Within four or five points, you have five teams and the second half will be exactly the same.
"Swansea play very well at home and away. We will need to be very strong in all senses, defending and attacking, if we want the three points."
Swansea v Manchester City is live on Sky Sports 1HD and Sky 3D from 12.30pm