City endured a frustrating afternoon against a spirited Hull side, who held out for more than an hour before Alvaro Negredo headed home and Yaya Toure netted a late free-kick.
And Pellegrini admitted that his charges need to work harder in order to compete this season, having fallen to a 3-2 defeat to another newly promoted side, Cardiff City, last week.
"The most important thing is getting the points," he said
"I am very happy that we won but of course I think we must improve. We had too many difficulties during the first half.
"Hull defended well and we need to try and be a dangerous team.
"Every match is hard and you must always concentrate and you must play 100 per cent to win any game in the Premier League.
"I know what the Premier League is, it's important to win 2-0. It's not easy to beat any team."
The Chilean was also unsurprised by the performance of striker Negredo, who was on hand to break the deadlock after 65 minutes, having entered the game as a half-time substitute.
Pellegrini also hinted the former Sevilla man could soon be handed a start having scored in two appearances from the bench so far this term.
He said: "I expect form Alvaro Negredo exactly what we are seeing, every time he plays.
"I know how good a striker he is.
"Everyone that puts in a good performance will have a possible start."
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