Rashford, 19, scored the opening goal in an impressive performance in United's 2-0 win against Chelsea at Old Trafford on Sunday following his selection as a striker ahead of Zlatan Ibrahimovic.
But Carragher reckons Chelsea's remaining fixtures are more favourable than Tottenham's, with Spurs still to play Arsenal and Manchester United.
United had conceded five goals and failed to score in its two losses to Chelsea this season - one in the league (4-0) and one in the FA Cup (1-0) - but Mourinho got his own back against his former club this time.
"We knew that playing this way would be very hard for them". "The league is open and we have a 50 percent probability to win [the title]".
Jose Mourinho has confirmed that he wants to add "more quality" to his Manchester United squad in the summer transfer window.More news: Cavs, Spurs ease into 2-0 leads
"Chelsea are still in the box seat", Mills said, as quoted by BBC Radio 5 Live's Twitter account.
Chelsea do face a tough away trip to Goodison Park, where Everton's home record is brilliant, and the Blues know the pressure is now on with Spurs only four points behind them in the title race.
"We have to dust ourselves off and prepare for a huge semi-final, and then we go again with some important home games coming up".
But Rashford had to wait only two more minutes to give his side the lead, keeping his cool after a superb through pass from Ander Herrera to slide the ball past Begovic.
"Yeah we are capable", he said.More news: FM: Parties in Korean Peninsula nuclear issue want no conflicts, wars
Chelsea was without first-choice goalkeeper Thibaut Courtois, who was injured, and wing back Marcos Alonso pulled out of the game during the warm-up after suffering from a virus during the week.
Much was riding on today's Old Trafford encounter, with the battle for Champions League football heating up as Antonio Conte's table-toppers attempt to ward off ever-improving Tottenham.
It doesn't matter if the leader is Chelsea or another.
Liverpool's Roberto Firmino, right, celebrates with teammate Philippe Coutinho after scoring his side's first goal during their English Premier League soccer match against West Bromwich Albion at The Hawthorns, West Bromwich, England, Sunday, April 16, 2017.
"We stay in a great position, but Tottenham are in good form and playing very well and with enthusiasm".More news: Paris shooting: Trump conveys condolence to France
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