The Manchester United frontman was sent off during the Three Lions' 2-2 draw with Montenegro in England's final Euro 2012 qualifier last week, and will be suspended for at least one match in the finals of the competition.
"What has Wayne Rooney done wrong? He's been sent off, it's not the first time and it certainly won't be the last," Gascoigne told talkSPORT.
"It must be a weight on him because he's so young, but he's probably the oldest in his team."
Despite Rooney's problems with restraint, the former England player believes that the 25-year-old will be handed the captain's armband one day.
"It won't be long before he's given the captaincy I suppose," Gascoigne added. "He's got to go to the Euros."
Meanwhile, the Republic of Ireland have been drawn against Estonia in the Euro 2012 play-offs.