Goals from Harry Wilson, Kamil Grosicki, Abel Hernandez and an own goal from goalkeeper Alex Smithies gave Hull victory before QPR had Nedum Onuoha sent off in stoppage time.
The result left the Tigers seven points clear of the drop zone on 44 points with five matches to go.
Hull have picked up five points from their last three matches, including creditable draws with Aston Villa and Wolves, and Adkins believes his team have to replicate their recent performances to avoid League One football.
Adkins said: “We need more points. The points we have now are not going to be enough. What are we on now, 45? 44? That’s not enough points to stay up.
“So we have to keep driving everybody to keep working hard for the next one. That’s the way I’m viewing it. Likewise, we want to be building towards next season.
“QPR have been in good form, excellent form, so we knew it was going to be challenging. For me it was a good result.
“My focus has been on ‘the next game is the most important one’, and that’s going to continue until the end of the season because I want to drive the level of performance that consistently gives ourselves an opportunity.”
QPR manager Ian Holloway said his side let down former player-manager Ray Wilkins, who died aged 61 on Wednesday.
Both sets of fans, in common with crowds at all the other games, paid tribute to the former England international with a minute’s applause before kick-off.
Hull City: McGregor, Aina, Dawson, Hector, Clark, Henriksen, Larsson, Bowen (Grosicki 52), Toral (Irvine 59), Wilson, Hernandez (Campbell 71). Unused substitutes: Meyler, Marshall, Tomori, MacDonald.
Queens Park Rangers: Smithies, Furlong, Onuoha, Lynch (Robinson 15), Bidwell, Luongo, Scowen, Manning (Sylla 46), Freeman, Wszolek (Samuel 67), Eze. Unused substitutes: Cousins, Ingram, Baptiste, Smyth.
Referee: G Eltringham (Tyne & Wear).