After suffering a shock loss at Cardiff last week, City were again troubled by one of the competition's newcomers but eventually ground out victory with two second-half goals.
Alvaro Negredo - strongly linked with Hull four years ago - came off the bench to break the deadlock in the 64th minute and Yaya Toure made the result certain with a late free-kick.
City failed to reproduce the brilliance of their season-opening demolition of Newcastle but Pellegrini was happy enough to accept the result.
The Chilean 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."
Negredo, signed from Sevilla for £20million this summer, has made a positive impression at City, having a goal disallowed against Newcastle, finding the target at Cardiff and then adding his latest effort against Hull.
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