Goals from Alvaro Negredo and Yaya Toure secured three valuable points for the 2012 Premier League Champions as they bounced back from a shock 3-2 defeat to Cardiff City last Sunday.
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"The most important thing is the points. In pre-season, we worked on different things but in the Premier League the most important thing is the three points, so in that sense I am happy with the win," he told reporters.
"But, of course, we must improve. We had too many difficulties getting a sight of the Hull goal. We lacked the movement that we need to be a dangerous team."
Pellegrini is under no illusions as to how difficult the Premier League can be and he admitted that last weekend's disappointment in the Welsh capital may have had a bearing on his team's display.
"The defeat against Cardiff could be one of the reasons that in the first half we didn't have the belief we could play but I think there are other important things.
"Every match in the Premier League is tough and you must be at 100% to win every match. Hull are a good team and, though I am concerned, 2-0 is still a good score."
The 59-year-old also revealed that he is expecting progress in a deal to bring Atletico Madrid defender Martin Demichelis to the club, while he was pleased to achieve a clean sheet after his defence - and goalkeeper Joe Hart in particular - were singled out for criticism during the reverse against Cardiff.
He added: "It [the clean sheet] is very important for the whole team, for Joe Hart and for our defenders. They weren't very confident after the last game so it was important for them."