After suffering a shock defeat away to Cardiff last week, City were again troubled by league 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.
Despite his satisfaction at picking up three points, Pellegrini was unhappy that City were unable to display the creativity they showed in their season-opening demolition of Newcastle.
The Chilean said: "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."
Hull can take many positives from their resilient display, including another fine performance by Scotland goalkeeper Allan McGregor, but they will rue an early miss by his former Rangers team-mate Sone Aluko. Danny Graham, replacing the suspended Yannick Sagbo, also struck early on only to see a flag raised for offside.
Pellegrini attempted to inject his side with fresh life at the start of the second half, sending on Negredo in place of Edin Dzeko.
The Spaniard broke the deadlock when his team-mate Pablo Zabaleta got behind the defence and sent an inviting cross to the striker, who moved into space and leapt high to plant a firm header past McGregor.
Toure then made the points safe in the final minute when City substitute Samir Nasri was fouled.