Chelsea scored with their first attack of the evening courtesy of Michy Batshuayi's deflected strike, yet could not add to their lead before the interval despite dominating possession and creating chances.
Hull were much improved after the break, and while former Tigers loanee Fikayo Tomori looked to have secured the visitors' progress with a back-post header shortly after the hour mark, wasteful Chelsea were unable to avoid a nervy finish as Kamil Grosicki's free-kick deflected in off Mateo Kovacic.
"With the chances we've had, we cannot concede in these circumstances and we have to control better," he told BT Sport.
"We want to go far but we could have handled better - it's not the first time we've not managed the game well.
"We had clear chances to score more and then we stopped playing our game and we got punished.
"If we want to fight for trophies we have to do better."