Liverpool are just one point behind Premiership leaders Manchester United, but the Red Devils still have a game in hand.
“This will have sent a message out to United and Chelsea,” said Carragher.
“Let’s not kid ourselves, they’d have been watching the game.
“When you play Real Madrid and Manchester United and score so many goals, you know in the back of your mind that can’t happen every week so to get five against Villa was a magnificent achievement.
“If we’d have dropped points against Villa, United’s defeat at Fulham wouldn’t have made that much of a difference but we’ve capitalised on it.
“Now United will realise they are in a fight for the league.”
“We are maturing and getting used to the demands of fighting for a title,” he continued.
“We were there earlier in the season but, having not been in that position before, maybe we didn’t know how to deal with it.
“We’ve probably found it difficult a few times this season to cope with that.
“We’re well aware that the title is in Manchester United’s hands, but we’re trying to put them under as much pressure as possible.”
