Adkins, who prepares to face his old club on Saturday, was controversially axed by Southampton in January and replaced by Argentine Mauricio Pochettino.
Reading go into Saturday's meeting of the two teams bottom of the table, while Southampton sit in 12th spot, four points above the drop zone, and Adkins believes he had helped set up the Saints for a good end to the season.
"I'm convinced they will finish in the top 10 because Andy Crosby, my assistant, and myself had prepared them to get to this position," said Adkins.
"We knew from the programme we implemented that they would become the fittest team in the division and that is the case.
"We knew we had good players and we were on a good run when we had a change, just two defeats in 12.
"All credit to the players, because they're the ones who have got to cross the white line. The professionalism they have shown has been phenomenal.
"We were down the bottom of League One when we started off and the guys have been fantastic.
"There is a good spirit and they have kept going. There was a good belief that Southampton would be there or thereabouts come the end of the season."
Adkins insists he bears no grudges against Pochettino despite the manner of his departure at St Mary's.
"I'll shake his hand and we will have a drink afterwards," added Adkins. "I bear no-one any grudges. I have nothing to prove.
"I had two-and-a-half years at Southampton in which we were very successful.
"It is a joy to watch them play and they have shown great professionalism.
"The players deserve the credit. I was proud, privileged and honoured to be their manager."