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.
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."
Hull boss Steve Bruce was pleased with his side's resilient display but was also left to rue the Tigers' bad luck.
Sone Aluko squandered a glorious chance to open the scoring in the early stages and Danny Graham had a good strike ruled out for offside.
Bruce said: "We are going to be rightly disappointed with the scoreline but I am immensely pleased with the way we played and the way we took them on. We couldn't have asked for anything more.
"Our Achilles heel, even last year in the Championship, was - can we score enough?
"You can see why we have come out of the Championship with the football we have played, but we need to score.
"We have had a big chance. Sone would have capped a wonderful performance from him if he stuck it away.
"Then the linesman gave an offside, which is right, but it was two inches offside, which I thought these days is supposed to go with the attacker.
"When you realised how close it is, it is a big call. You need that little bit of luck when you come here but it wasn't to be."
Bruce had his head in his hands on more than one occasion but joked when asked about it.
The former Manchester United defender said: "I was covering myself because of the abuse I took. I don't like being called the elephant man!"
Both clubs are looking to strengthen before Monday's transfer deadline with the home side strongly linked with Atletico Madrid defender Martin Demichelis, who played for Pellegrini at Malaga.
Pellegrini said: "I expect it (some business). I hope for one defender. Maybe that is the name we want. We will see what happens."
Hull have been linked with a move for Arsenal striker Nicklas Bendtner, who played for Bruce at two of his previous clubs.
Bruce said: "I've had him twice before and he did very well at Birmingham and Sunderland, but can we get him to come to us and can we afford him?
"It is difficult for us. He plays for Arsenal and we have just come out of the Championship. We will see.
"It is very difficult but we will keep working at it and see what we can come up with in the next 48 hours - and then put an end to the madness which has been this window."