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 make it to the fourth round for the sixth season in the last seven.
It provided respite from their league 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 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 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.
“Ultimately it’s gone the other way but I’ve got no regrets on the selection of the team.
“Parts of the game I was disappointed in. The last half-hour was really good, first 10 minutes were really good. I think the worst result would have been a draw. Disappointed? Yes, but we move on now to the 21 cup finals we’ve got.”