Carragher made his comments following Sunday's 4-1 thrashing of West Ham by Villa.
For the eleventh consecutive home victory, Unai Emery's team scored three goals: Leon Bailey, Ollie Watkins, and Douglas Luiz.
After nine games, Villa has risen to fifth place in the standings, just two points behind Manchester City.
It has generated speculation that they might place in the top four, beating out teams like Chelsea and Manchester United.
"When you reflect on last season, you consider what Newcastle accomplished in terms of Champions League qualification. And they received the adage "they won't get there" during the entire season. But they did in the end.
"Aston Villa will find it difficult. Since they play European football, their main obstacle to qualifying for the Champions League will be different from Newcastle's from the previous season.
The manager's track record in Europe makes me believe they'll succeed in that league, thus there will be a lot of Thursday-Sunday games after Christmas. They may not have any other issues, Carragher said Sky Sports.
