Sir Alex Ferguson believes the race for the Premier League title is now only between Manchester United and Liverpool.
Second-placed Liverpool, five points adrift, are the nearest challengers to leaders United, with Chelsea in fourth and Arsenal fifth.
Reds defender Carragher told his club's website: "It looks like it is going to be us and Manchester United."
United manager Ferguson said Chelsea's sacking of Luiz Felipe Scolari "played into our hands".
Guus Hiddink was appointed Chelsea's temporary boss last week and insisted the club's title hopes were not over.
But Ferguson disagreed, saying:
"The title race now is going to be between ourselves and Liverpool. However, I shall be keeping a wary eye on Aston Villa, who seem to have picked up the baton from Arsenal. I was shocked that Chelsea should part so soon with a manager of such great experience and proven success as Scolari.
"Their haste is a reflection of the sad way the game is going, with everyone from owners, the board members, the supporters and the media demanding instant success and showing absolutely no patience in the pursuit of their ambition. Chelsea have called in a very experienced manager in Guus Hiddink and I am sure he will make an impact. At the same time, he has to start from scratch, perhaps putting together his own staff and gathering round him players of his choice which may take him some time."
Defending champions United extended their lead at the top of the table after a routine 3-0 victory over Fulham on Wednesday.
And United's win over Roy Hodgson's men at Old Trafford left title rivals Chelsea 10 points off the pace and Arsenal 15 points adrift.
"You can never be dead sure but it is fair to say Chelsea have an uphill fight now," added Ferguson after the victory.
"Things can happen. We were 12 points clear of Arsenal in 1998 but we got a lot of injuries and lost the league. Now we can cope with it, like we have done in the last few weeks."
Meanwhile, Liverpool defender Jamie Carragher said Liverpool had not given up hope of ending their own title drought. It is 19 years since Liverpool last won the league title, but Carragher believes the Reds are in with a chance of ending that streak this season.
"We finished fourth last season, but we have overtaken Chelsea and Arsenal, even though everyone at the club understands that it's not over yet by a long way," he said.
"Just by overtaking Chelsea and Arsenal in the challenge is an achievement in itself already so everyone should be proud of that.
"A lot of people said at the start of the season that we needed to be in the title race at the end and at least be in with a fighting chance. Now hopefully we can go one step further and win this title. There are still a lot of games to go, so it's important everyone at the club remains calm."