England's all-time leading goalscorer Rooney was overlooked on Thursday because of other players' "good form".
The 31-year-old was left out of the previous squad in March due to injury.
"There are only so many times you can speak about it," said Southgate, who has not yet decided on a new captain.
Southgate added it was "impossible to say" whether Manchester United striker Rooney, who has scored 53 goals in 119 international appearances, would play for England again and that "form will dictate" his inclusion.
"I certainly don't rule it out because a player of his quality and experience, you hope he will reach the levels we know he can and be a big part of England's future," Southgate told BBC Radio 5 live.
"I'm mindful of being respectful of what he's done so don't like talking about him in the past tense.
"Knowing Wayne and his mentality he'll want to prove people wrong, prove me wrong and he's more than capable of doing that."
Rooney has started only 15 Premier League games for the Red Devils this season.
"I've no idea what the future is for Wayne at Manchester United so it's impossible for me to comment if he's part of the plans or not," added Southgate.
"He's got some big decisions to make this summer - you want your players playing in the biggest possible games."
Rooney has said he has "more or less" decided his future at Old Trafford and that he would only move to former club Everton if he stays in the Premier League.
Southgate also confirmed that Liverpool right-back Nathaniel Clyne has pulled out of the squad due to injury, with Tottenham right-backs Kyle Walker and Kieran Trippier already included.
England face Scotland at Hampden Park in a Group F qualifier on 10 June before travelling to France for a friendly on 13 June.
In Rooney's absence in March, centre-back Gary Cahill was captain in friendly defeat by Germany, while goalkeeper Joe Hart led the side in victory over Lithuania in the World Cup qualifier at Wembley.
However, Southgate said there are a "number of different ways" he could go when choosing his next captain.
"There are a lot of potential leaders emerging from this group and that's good because there's always been a focus on one person and an over-reliance on one person," he said.
Southgate said he has a "clear idea" of his starting side for the Scotland match, apart from a "couple of positions" he wants to look at in training.
However, he added: "Not many people are guaranteed their places."
Goalkeepers:
Jack Butland (Stoke), Fraser Forster (Southampton), Joe Hart (Man City), Tom Heaton (Burnley)
Defenders:
Ryan Bertrand (Southampton), Gary Cahill (Chelsea), Aaron Cresswell (West Ham), Ben Gibson (Middlesbrough), Phil Jones (Man Utd), Chris Smalling (Man Utd), John Stones (Man City), Kieran Trippier (Tottenham), Kyle Walker (Tottenham)
Midfielders:
Dele Alli (Tottenham), Eric Dier (Tottenham), Adam Lallana (Liverpool), Jesse Lingard (Man Utd), Jake Livermore (West Brom), Alex Oxlade-Chamberlain (Arsenal), Raheem Sterling (Man City)
Forwards:
Jermain Defoe (Sunderland), Harry Kane (Tottenham), Marcus Rashford (Man Utd), Jamie Vardy (Leicester)
England manager Gareth Southgate says he did not speak to captain Wayne Rooney before leaving him out of the squad for June's matches with Scotland and France.