Stoke City claimed their first win of the season after James McClean gave them the lead and Mame Biram Diouf’s effort looped into the bottom corner after deflecting off Tigers defender Jordy de Wijs.
Hull had Evandro sent off on the hour mark for a dangerous tackle after reacting to a challenge from Joe Allen.
Adkins said: “We’ve come away from home and we’ve conceded a goal from a corner and we have to address that, I feel.
“I felt David Marshall dealt with the first ball in, punched it really well. It’s gone outside the penalty area and McClean has driven it back in. It’s gone through two people’s sets of legs, and the second one is deflected, so we didn’t get the rub of the green.
“I think we started the second half well. I’m looking to make two substitutions – I have Will Keane and Nouha Dicko waiting to come on while I take off Evandro and Fraizer Campbell – but as they are stood waiting Evandro gets sent off.
“Having wanted to get back into the game, we were 2-0 down with 10 men so it was always going to be challenging.”
Stoke’s first goal came nine minutes in when the ball dropped to McClean on the edge of the penalty area after Hull failed to fully clear Allen’s pass from the left. The Irishman struck left-footed through a crowd of players, beating Tigers goalkeeper David Marshall.
Hull responded and Evandro’s volley was directed straight at home goalkeeper Jack Butland, then Fraizer Campbell sliced his swivelling shot wide.
Stoke should have been further in front at half-time, going close through captain Ryan Shawcross, who glanced Allen’s corner wide, while Saido Berahino could only aim his thumping attempt off target. When the game resumed after the break, Stoke tried to kill off the contest.
Marshall had to be at his best to keep out headers in quick succession from Cuco Martina and Diouf prior to the hosts going 2-0 up.
A sweeping move ended with Diouf’s 59th-minute shot at goal being deflected into the net with the help of defender De Wijs, with the ball finding the corner of Marshall’s net.
Stoke City: Butland, Martina, Shawcross, Martins Indi, Pieters, Diouf (Bauer 88), Allen, Etebo, McClean, Berahino (Krkic 80), Crouch (Afobe 80). Unused substitutes: Adam, Fletcher, Federici, Soutar.
Hull City: Marshall, Lichaj, Burke, De Wijs, Kingsley, Bowen (Stewart 78), Henriksen, Batty, Kane (Keane 67), Evandro, Campbell (Dicko 63). Unused substitutes: Toral, Long, Curry, McKenzie.
Referee: Darren Bond (Lancashire).