City battled to a 2-0 win thanks to goals from Alvaro Negredo and Yaya Toure.
Pellegrini said: "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."
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