Adkins refused to be downcast after the 1-0 defeat to Bristol City - a game his side had chances to win - and made it clear he still has complete faith in his squad.
He said: “I am not hiding from where we are in the table and I understand that it will be highlighted by the fans and media.
“But if we keep doing the same things our position will improve. The supporters who travelled saw a committed display and we just needed to take our chances.
“We have been playing consistently well against some top sides and there is no shortage of character among the players.
“We could have been ahead in the first couple of minutes when the Bristol keeper has made a fantastic save and we just couldn’t take one of the opportunities we created.
“We had to reorganise because of injuries and I thought the players concerned did really well. It’s important that we keep believing in ourselves.
“I can’t ask for more in terms of effort, but of course we need to turn performances into points as soon as possible.”
Hull goalkeeper David Marshall, who had made some fine saves, could only parry a shot from substitute Matty Taylor and Famara Diedhiou nodded home the rebound from 10 yards to secure all three points.
It was rough justice for a Hull side who had contributed much to an open game and who had been hit by a stoppage-time equaliser in their 1-1 draw with Preston on Saturday. But Bristol created more chances and just about deserved the points.
The corresponding match last season ended 5-5 and there were enough chances for both sides in an entertaining first half for a repeat of that scoreline.
Hull could have been ahead inside two minutes when Todd Kane eluded a weak challenge from Jay Dasilva and crossed for Kamil Grosicki, whose close-range shot brought a fine save on his line from Max O’Leary.
Chris Martin sent an overhead kick wide and Grosicki firing across goal with no team-mate able to get a touch.
Josh Brownhill saw a right-footed shot from 20 yards hit the foot of an upright and the only surprise at half-time was that neither side had capitalised on some slick, attacking football and some poor defending. Straight after the interval Hull’s Tommy Elphick headed just wide from a right wing corner.
Marshall produced a stunning save at full stretch to keep out a deflected shot from Tomas Kalas as Bristol City began to turn up the heat.
Chances had dried up and the home crowd were getting frustrated. Bristol City coach Lee Johnson also made three second-half changes in a bid to find a cutting edge. Fraizer Campbell headed wide when unmarked for Hull just after seven minutes of stoppage time had been signalled.
It proved a costly error as Diedhiou settled the match, with Taylor having another shot saved by Marshall in a thrilling finale.
Bristol City: O’Leary, Hunt, Kalas, Webster, Dasilva, Eliasson (Watkins 78), Brownhill, Pack, Paterson (Taylor 84), Diedhiou, Weimann (O’Dowda 58). Unused substitutes: Walsh, Hegeler, Kelly, Wollacott.
Hull City: Marshall, Burke (McKenzie 60), Elphick, De Wijs (Campbell 73), Kane, Irvine, Batty, Lichaj, Bowen, Martin (Dicko 66), Grosicki. Unused substitutes: Long, Keane, Fleming, Sheaf.
Referee: P Banks (Norwich).