Fraizer Campbell’s seventh-minute strike settled a keenly-contested encounter in which Bolton lacked the attacking acumen to seriously trouble Hull goalkeeper David Marshall, who kept a welcome clean sheet.
Despite Saturday’s win, Hull remain in the Championship relegation zone and had lost their previous five away games.
But Tigers boss Adkins is adamant his team deserved more from recent performances.
He said: “We’ve created a lot of chances in the last run of games we’ve had and here we’ve come away from home and kept a clean sheet.
“You could see there’s a spirit and togetherness amongst the players – everyone contributed.
“The culture at the training ground has been exceptional. We’ve got characters and we treat them well. We work them very hard and demand a lot from them, but everyone enjoys coming into work.
“Things have maybe gone against us a little bit but we prepare for every game.
“On a daily basis we’ve got everyone contributing,” said Adkins. “I’m always optimistic about what we do. We’ve got a team and a belonging here.
“These are the times when you find out about the people you’ve got around you.
“We scored early for a change. It was a good finish from Fraizer Campbell.
“We’ve created a lot of opportunities early in previous games and this time we’ve taken one.”
With just one win from their last 11 Sky Bet Championship games, former Bradford City boss Parkinson’s team were jeered off the pitch by factions of frustrated home supporters.
Bolton Wanderers: Alnwick, Wilson, Hobbs, Beevers, Olkowski (Magennis 81), Joe Williams, Vela, Dyer (Buckley 67), Oztumer, Donaldson, Doidge. Unused substitutes: Little, Taylor, Murphy, Matthews, Wheater.
Hull City: Marshall, Lichaj, Elphick, McKenzie, Kingsley, Bowen (Mazuch 66), Batty (Stewart 80), Irvine, Henriksen, Grosicki (Dicko 72), Campbell. Unused substitutes: Long, Kane, Keane, Martin.
Referee: D Webb (County Durham).