Alex Ferguson’s side have seen Liverpool cut their Premier League lead from seven points to just one.
Carragher roared: “United will realise they are in a fight for the league now.
"We’re the form team, and this is the best time of the season to be in form.
"There’s not long to go now and hopefully we can keep it going — but United will know now that we are in there.”
Liverpool gave Aston Villa a 5-0 whacking on Sunday after beating United 4-1 at Old Trafford and putting four past Real Madrid in Europe.
The Reds capitalised on United and Chelsea both losing on Saturday and Carragher added: “It’s not normal for results to go for you at the top, so it put more pressure on us.
“Earlier in the season, we hadn’t been at the top before and we didn’t know how to deal with it.
“But we are maturing and getting used to the demands of fighting for a title.”
United have played a game less and Carra added: “One point with a game in hand is a decent lead. We’ve just got to stay on their coat-tails.”