England’s record scorer and most-capped male outfield player, with 53 goals in 117 appearances, Rooney has netted once in 12 games for club and country this season.
“My game now? Of course, I’m not denying it is in a difficult period. I’ve been on the bench the last few games for Manchester United but that’s part of football,” said Rooney.
“I have to work hard and, when I’m needed for both club and country, I’ll make sure I’m ready.”
Tottenham’s Eric Dier will replace Rooney in midfield against Slovenia.
Southgate added: “We have looked at the way Slovenia play and I knew in my mind the profile of the midfield I wanted to play in this game. In no way is it a reflection of Wayne’s performance on Saturday.
“He had a lot of the ball and played with great tactical discipline. It’s not an easy decision to take because of the respect I have for him as the captain of this team.”
Rooney said being dropped by England had not changed his plans to retire from international football after the 2018 World Cup in Russia.
Asked if he was surprised to be left out, he added: “No, I think it is football.
“I’ve played 13 years non-stop for England and given everything. A time comes when you’re not the first name on the team sheet, which I have been in the past.”
Rooney also praised Henderson, 26, who succeeded Steven Gerrard as Liverpool captain.
“I think Jordan is a fantastic leader,” added Rooney. “He has taken a difficult job from Steven Gerrard and grown into the position.
“He has great leadership qualities and he deserves his chance. It will be an incredibly proud moment for him and his family.”
11 – Playing four games as a forward and six in midfield, Rooney has had more shots on target than any other England player over their past 10 appearances. Daniel Sturridge has had 10, Harry Kane nine.
550 – Rooney has made the second most number of passes of any England player over the past 10 appearances. Only Jordan Henderson has more with 628. Dier has made 545.
85.09 – Rooney’s pass accuracy percentage is the fifth best of any England player over the past 10 games, beaten by Dier (90.09), Ross Barkley (88.92), Henderson (88.22) and Theo Walcott (87.02).
Settled position would help – Rooney
Rooney has mainly played in an advanced midfield role for United this season, but deeper for England.
Asked if his game would benefit from a settled position, he replied: “It would, of course. But that’s the managers’ decision where they want me to play.
“I am not naive in terms of thinking that I am still a 20-year-old who could do what I could do when I was 20.
“I am 30 years of age. I am not 35 or 36 where you are thinking, ‘can you get back from it?’ I feel fine.
“[Manchester United great] Ryan Giggs at 30 wasn’t the same player as at 18 – and he played till he was 40. Players re-evaluate and work out the best way to move forwards. I’m sure that will happen with me.
“After the summer it would have been easy for me to walk away and say: ‘That’s it, I’ve had enough.’ But that’s not me.”
We haven’t looked after Wayne – Southgate
Southgate said he did not like the idea of “satisfying” Rooney’s critics by dropping his captain, and said he was “more annoyed” than Rooney by the negative reaction.
“There is a thing of respect and unfortunately very often we don’t see it fully until players retire and they are finished. I know that is the case,” he said.
Southgate said he remembered former England boss Sven-Goran Eriksson saying of a young Rooney: “Look after him, he’s your future.”