The Tigers avoided an upset when on-loan Chelsea defender Ola Aina headed home at the far post in the 58th minute for his first senior goal, which ensured Hull made it to the fourth round for the sixth season in the last seven.
It provided respite from their Championship struggles, and after ending a run of three consecutive away defeats, Adkins was pleased with the resilience that secured a second clean sheet on the road this season.
He said: “We’ve played against a good side in Blackburn, you see them at the top of the league. Both teams obviously made a few changes. I thought in the first half, probably for 35 minutes, we played some exquisite football. We just missed that final bit of putting the ball in the back of the net, with some of the football we played.
“In the second half, we scored a goal from a set-play. Obviously, when they put (Danny) Graham on, they were a bit more threatening, putting balls in especially from deep. But we’ve had to show that resilience, and block things to see out the game and the lads have gone and done that.
“Our performances have been excellent of late. We’ve been on the wrong end of a 1-0 defeat with some good performances. But today we’ve won the game, so it helps with the spirit moving forward.”
Defeat ended Blackburn’s 18-match unbeaten run. They had the momentum following the introductions of Bradley Dack and Graham, who missed the best chance of the game.
Despite this, Tony Mowbray had no regrets, as promotion from League One remains his priority. He said: “I think that’s always a call that managers make. Our main target is to get out of this division and win league matches, so (Richie) Smallwood, probably our best player this year, wasn’t even in the 18.
“We can’t afford to lose Bradley Dack, Danny Graham, Richie Smallwood, Paul Downing, (Charlie) Mulgrew was touch and go, yet I feel if we’d have played a team of under-23s, it wouldn’t have been the right thing to do because I thought we might have been able to sneak home with a 1-0 win.”
Blackburn Rovers: Leutwiler, Caddis, Nyambe, Mulgrew, Williams, Bennett, Tomlinson (Dack 61), Evans (Travis 43), Conway, Nuttall (Graham 61), Samuel. Unused substitutes: Raya, Hart, Downing, Wharton.
Hull City: Marshall, Aina, Hector, Tomori, Clark, Henriksen, Stewart (Meyler 80), Bowen, Evandro (Irvine 61), Toral, Diomande (Campbell 76). Unused substitutes: McGregor, Dicko, Clackstone, Hamilton.
Referee: O Langford (W Midlands).