The visitors played their part in an entertaining contest and could have taken the lead on more than one occasion.
Hull had the first real opportunity to break the deadlock after Bluebirds goalkeeper Neil Etheridge spilled a Kamil Grosicki free-kick, but Jon Toral failed to capitalise with a weak effort.
Nouha Dicko then snuck in behind the Cardiff defence and poked an effort against the post and the hosts survived.
Lee Tomlin looked like he was going to be the man to find the creative spark when he stung the hands of Allan McGregor.
But the deadlock was finally broken 12 minutes into the second period thanks to Cardiff captain Bamba, who got his head to Anthony Pilkington’s flick-on after Tomlin’s inch perfect cross.
Hull manager Adkins - who enjoyed a 3-2 home wib over Brentford in his first game in charge last week - praised his players for their effort as they bid to pull away from the wrong end of the table.
He said: “They’re flying high an they’re difficult to play against. But we started well, and for a club who are down the bottom we got on the front foot and caused them problems.
“They started dominating down the right hand side, I thought (Nathaniel) Mendez Laing was a massive threat for them, it was like a war of attrition.
“I don’t think it was a free-kick leading up to their goal and Bamba was a fraction offside for their goal.
“You need those decisions to go your way but it didn’t today. I couldn’t ask for more than what the players gave me today.
“Sometimes you get the decisions and sometimes you don’t. Many teams have been rolled over here this season, but we competed which is the important message.
“On Wednesday we only had 17 players available, we’re going to have to make a lot of changes over the festive period and then hopefully it settles down.”