The former Arsenal captain was on Monday celebrating his 28th birthday as a Premier League winner for the first time after Sunday's 1-0 defeat of Crystal Palace at Stamford Bridge.
Fabregas joined Chelsea from Barcelona last summer, having previously spent eight years and made more than 300 appearances with Arsenal, and has played a key role in the Blues' first title in five years.
Now he wants more.
"The Premier League has always been a trophy that I wanted to get in my career
Hopefully it will be the first of many," Fabregas told Chelsea TV.
"I hope the future holds many trophies, many Premier Leagues, Champions Leagues and hopefully we can start building a fantastic team that next year can fight for the Premier League and Champions League.
"It feels great
It's the feeling that I really wanted to get
It's a special moment, a special trophy
The most difficult league in the world, so very proud."
Chelsea's domestic duty was aided by their last-16 Champions League elimination to Paris St Germain.
The Blues, who won the Capital One Cup in March, led from the opening round of fixtures and Fabregas insisted that consistency set them apart from their title rivals.
The Spain playmaker added: "The consistency has been key
We didn't allow other teams to get on top of us and to make us doubt ourselves.
"We never game them any chance, really
It's been probably one of the best Premier Leagues that a team can have."
Fabregas paid tribute to Mourinho, who persuaded him to move to Stamford Bridge from Barcelona, promising silverware.
The 2010 World Cup winner said: "I can understand the pressure he's under
He's the best manager and he has to get results and he always manages to do that.
"With any squad he's been with he's always managed to get results, to get his team to be champion and that's the sign of a real winner, a real professional."
Source : PA
Source: PA