The Lilywhites were handed only their third home league defeat of the season as Hull midfielder Jackson Irvine struck in the first half to give his side the lead.
Alan Browne equalised with a spectacular second-half effort but Irvine settled the points with his second goal 10 minutes from time as in-form Hull leapfrogged the Lilywhites to move up to 15th.
Adkins said: “I thought we were very good in the first half. I thought Grosicki [Kamil] was linking up well with Jackson Irvine for periods and it was a beautiful cross from [Stephen] Kingsley for Jackson to get the first goal.
“Second half we knew they were going to come firing at us, it’s always going to be a competitive place to come with the present Preston side.
“I’m disappointed with the goal because we lost position in the middle of the field and they’ve gone and scored from it.
“The crowd, which we kept quiet for long periods of the game, were loud and created a great atmosphere for us. It was challenging but we stuck at it.
“We’ve got a challenging game against Leeds now but we’ve got to go to Elland Road and take the game to them, against the league leaders. It’s all to gain.”
Grosicki fired wide early on but the Tigers went 1-0 up as Irvine powerfully headed home from Kingsley’s ball on 28 minutes.
Parity was restored when Browne’s spectacular hit-and-hope strike sailed into the top-right corner from outside of the area on 47 minutes.
The Tigers knocked on the door for victory and got their reward as Irvine got the deciding touch on a Tommy Elphick corner, sneaking in at the far post to claim the points.
Preston boss Alex Neil said : “Both teams played the same way with the same formation.
“They did it because they’re away from home and we did it because we’re lacking in numbers at the top end of the pitch.”
Preston North End: Rudd, Clarke (Fisher 83), Huntington, Davies (Storey 35), Hughes, Gallagher, Johnson, Burke (Ledson 46), Browne, Barkhuizen, Nmecha. Unused substitutes: Crowe, Woods, Simpson, Walker.
Hull City: Marshall, Kane, Elphick, De Wijs, Kingsley, Bowen (Lichaj 90), Henriksen, Stewart, Grosicki (Burke 90), Irvine, Campbell (Martin 86). Unused substitutes: Dicko, Long, Batty, McKenzie.
Referee: S Duncan (Tyne & Wear).