Second-half goals from substitute Alvaro Negredo and Yaya Toure secured the points for City and provided a winning response to last weekend's shock defeat at Cardiff City.
However, in the absence of Vincent Kompany, the hosts again looked shaky at the back, especially in the first half, and Pellegrini has been strongly linked with a move for Atletico Madrid defender Martin Demichelis.
Pellegrini said: "I expect it (some business). I hope for one defender. Maybe that is the name we want. We will see what happens."
Regarding the victory over Hull, Pellegrini felt his team had done their job after making it two wins out of two at the Etihad Stadium.
The Chilean added: "First of all, the most important (thing) is the points.
"In our friendly matches in pre-season we tried to work on different things, but when we start the Premier League the most important thing is to win the three points.
"I am very happy with the win but of course I think we must improve. We had too many difficulties in the first half (in creating chances) to shoot at the Hull goal.
"They defended very well and without the movement, we need to try to be a dangerous team.
"Everyone told me last week (after) we lost a game to two set-pieces that I now know the Premier League.
"But I know the Premier League is very difficult every match. You must concentrate and play 100 per cent to beat any team.
"I am concerned but 2-0 is a good score. We can't win every game 4-0 or 5-0. The Premier League is tough."
Negredo, signed from Sevilla, has made a positive impression, having a goal disallowed against Newcastle and then finding the target at Cardiff before his effort against Hull.
Pellegrini said: "I expect from Alvaro Negredo exactly what we are seeing every time he plays.
"I know how good a striker he is. With Alvaro and Edin (Dzeko) we have two very good strikers and we need both of them."