Adkins' first win as Royals boss came more than five weeks after his appointment and ended an 11-match winless run, which included nine defeats.
Hal Robson-Kanu bagged a brace at Craven Cottage while Adam Le Fondre and Jem Karacan were also on target in a thrilling clash.
"We know where we are in the division," Adkins said. "The attitude and application from the players since I joined the club has been first class.
"We saw here another steady progression in what we've wanted to do over a short space of time.
"It is evolving well, which I think is important. To score four goals away from home in the Barclays Premier League is no mean feat.
"I thought it was an entertaining game for the supporters - really, really good.
"We are delighted because we've got that winning mentality, winning feeling back, which is important.
"Again, it is the progression of moving forward, which we are looking to build on. I am asking the players to play a way where we can build out from the back, build through the field of play. The players have controlled the ball better in that respect and it is about progression."
- Sports & Recreation
- Adam Le Fondre
- Jem Karacan