Manager Giggs has been absent from the last two Wales camps after being arrested on suspicion of assault.
Page has won four and drawn one of the six games in Giggs' absence, with Tuesday's 1-0 home win over the Czech Republic kick-starting their World Cup qualifying campaign after an opening defeat by group favourites Belgium.
"He's been unbelievable," winger James said of Page after his first headed goal in senior football had secured Wales' victory late on in Cardiff.
"He's been great and he's taken the role very well. Him and Albert (Stuivenberg, Page's assistant) have been unbelievable in getting things across to us. That shows in the game."
Asked if Page could step up if Giggs remained absent this summer, James said: "Yes, definitely.
"Whether he's the manager or not, he's been such a big part of before when the gaffer has been here. But he's taken on the role so well. Nothing has changed really.
"He has just been doing the job that he was doing before. He gets the points across to us so well.
"Him, Albert and all the staff behind him have been unbelievable."
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