Rickie Lambert scored his fifth Premier League goal of the season when he headed in the opener, before Jason Puncheon doubled the visitors’ lead in the 43rd minute.
Adkins’ side managed to temper a brief Hoops resurgence when Junior Hoilett halved the deficit, before Anton Ferdinand’s own goal wrapped up three points in the 83rd minute.
“We knew at half-time that QPR would come straight at us after the break but the players dealt with the situation very well. We had good game-management,” Adkins told BBC Sport.
Adkins is second favourite, behind Mark Hughes, to be the first Premier League manager sacked this term, with the Saints in 19th position.
But the 47-year-old is adamant everyone is sticking together at the club, with the south coast club now just a point behind 17th-placed Reading.
“The fans lifted the players all the way through the game. We’re all together, we’re working hard for everyone and it was a great afternoon for us. We are all supporting each other. Everyone is together at our football club,” he added.