The West London club took another early lead through Morgan Rogers’ seventh minute strike, his third of the season.
Chelsea have now opened the scoring within the first four minutes in all of their four Premier League games so far in 2026-27.
Despite that, Hull fought back and were 2-1 up heading into half-time. Joao Pedro then restored parity just after the hour mark, and the spoils were shared.
Speaking to BBC Sport after the game, Alonso insisted his side got the result they deserved.
"We're disapointed with the result. We wanted to win. We have to be disappointed with some parts of the performance especially when we had the lead,” he said.
"We were too soft for the equaliser. We can do much better.
"(Playing well for) 15 to 20 minutes is not enough. You have to be on your top for 90 minutes. There are times we're not able to keep that momentum and intensity. We could have done more for sure because we had chances.
"We had one or two good chances to get the winner but you're still open. Not happy. We can do better. We got what we deserved.
"We need to be more solid and be more controlled. New players and new staff. This is the process. In a few months I'm sure we'll be able to control better."
Chelsea will travel to Keith Andrews’ impressive Brentford side as they seek to keep up with Man City and Arsenal on Friday (September 18).