A 32nd-minute strike by Andrew Crofts sent the Royals diving to their fourth defeat in the last five matches as Brighton clinched a 1-0 win at the Amex Stadium.
Adkins felt speculation linking him with the West Brom job had simply come from bookmakers shortening the odds.
He said: "The bookmakers are covering themselves and this has come out of the blue. West Brom don't have a manager but all my focus is to try and improve Reading. All the energy and focus is to us.
"I wanted a good cup run but unfortunately a deflected goal has done us today."
Reading have only scored five goals in their last eight games and Adkins believes the club have no option but to be active in this month's transfer window if they want to have a successful second half of the season.
He added: "We've got a fantastic board and the chairman will do everything that is right for the club. We've got to let the board get on with it.
"We've got an opportunity to regroup and maybe get one or two in because our focus is to get promoted."
Brighton assistant head coach Nathan Jones praised the way his team responded after eight changes were made.
"We genuinely used our squad," he said. "We have a fantastic squad which we are very proud of and we haven't finished one game over the Christmas period lacking energy.
"We were unfortunate not to win them all. We are happy with the performance more than anything and were reasonably dominant in the first half."
Brighton called up midfielder Solly March for his first league start and Jones felt the youngster reacted to the opportunity superbly.
He added: "Solly has been chomping on the bit to play and it was time to put him in.
"He needs games for his own development with us or on loan. We wanted to put him in earlier but he's come to the fore in this game."
Jones also played down reports linking Liam Bridcutt and Will Buckley with moves to Sunderland, with speculation suggesting that former Seagulls boss Gus Poyet is set to raid his old club in the January transfer window.
"They are Brighton players," he said. "We are looking to progress to get to where we want to be and we need good players for that."