Forest are now just two points off the top six thanks to an ultimately convincing triumph at the City Ground.
There had been little to choose between the two sides in a scrappy first half, but Forest cut loose after the restart by scoring three times in quick succession through Joao Carvalho, Karim Ansarifard and Joe Lolley.
Adkins, however, said: “Before the game, we were four points off the play-offs and now we are five points.
“We’ll reflect on this and prepare for the next game at top-of-the-table Norwich. We kept the home crowd quiet for long periods, but maybe we didn’t have that final decisive pass in the final third.
“The first goal was going to be decisive but it’s fair to say it was a wonder strike from the lad.
“Sometimes it’s fine margins, but that’s given the home side the impetus to win the game – and then the second goal has taken it away from us.
“The scoreline’s the wrong one, but for long periods we were well and truly in the game.
“We wanted to win and we played some good football again, but you’ve got to go and score.”
Counterpart Martin O’Neill said: “We’re in the (play-off) battle. It’s a still a long road, but these next two games (at home to Aston Villa and away to Ipswich) are big for us before the international break.”
Nottingham Forest: Pantilimon, Darikwa, Milosevic, Benalouane, Osborn, Pele, Yates, Colback, Lolley (Goncalves 87), Leo Bonatini (Ansarifard 59), Murphy (Joao Carvalho 68). Unused substitutes: Guedioura, Watson, Wague, Steele.
Hull City: Marshall, Kane, Burke, De Wijs, Lichaj, Bowen, Henriksen, Irvine, Grosicki, Pugh (Evandro 54), Martin (Campbell 54). Unused substitutes: Stewart, Milinkovic, Long, McKenzie, Ridgewell.
Referee: J Linington (Isle of Wight).