Mourinho clinched his first piece of major silverware since winning La Liga with Real Madrid in 2012 courtesy of a 2-0 success over Tottenham at Wembley on Sunday.
Manchester City's 2-1 defeat at Liverpool earlier in the day left Chelsea's five-point advantage at the top of the table intact.
And the leaders now head to Upton Park as they continue their quest for a fourth Premier League crown, and third under Mourinho.
"It's in the hands of everyone," the Portuguese said. "We have lots of difficult matches to play. City have difficult matches.
"[Manchester United] are in the title race too. Liverpool [beating City], I predicted that."
Mourinho also revealed how he attempted to shield his players from events at Anfield as they prepared for their Wembley date with Spurs.
"I knew that was an impossible mission, but I didn't want the television on in the hotel or on the bus," he added.
"I told them I didn't want any kind of manifestation or disappointment if City scored in the last minute, or Liverpool won. I wanted complete silence.
"We were successful on that. But one member of my staff jumped up in the bus. Silvino [Louro, assistant first-team coach]. I wanted to kill the guy. He broke the rule."
Chelsea are unbeaten in their last six league outings, although they were disappointed to be held to a 1-1 draw by struggling Burnley on February 21.
West Ham, meanwhile, have not won any of their last six games in all competitions and were beaten 3-1 at home by Crystal Palace on Saturday.
Goalkeeper Adrian has previous experience of frustrating the Chelsea boss - helping former club Real Betis to a 1-0 win over Mourinho's Real in 2012, before putting in another superb display in a goalless draw at Stamford Bridge last season.
"I don’t know if Mourinho remembers me but when I play against him I have got some good results," the Spaniard told West Ham's official website.
"Personally, I feel good when I play against Mourinho!"
The visitors will continue to be without Nemanja Matic, who serves the last instalment of a two-match ban for his red card against Burnley, while fellow midfielder John Obi Mikel is a doubt with a knee problem.
For West Ham, Morgan Amalfitano is still suspended after his dismissal against West Brom in the FA Cup, and Carlton Cole's hamstring injury means he remains a fitness concern for manager Sam Allardyce.
