Adkins was unable to prevent the Royals' relegation from the Premier League after being appointed in late March.
But the former Southampton chief is already looking forward to the challenge that awaits next season.
"We know it will be very competitive in the Championship, every club wants to be up there. Practically every team in there has already been in the Premier League," he told the club's official website.
"We want to be back in the top flight as soon as possible, we've got players here who've gone course and distance and won the Championship last year so that's a positive for us.
"I've got belief in my own ability but I know you can't do it all on your own. We will push everyone, have the mentality to be the best and we've all got to do it together."