Mathieu's transfer from Valencia to Barcelona was met with some criticism last week due to the €20 million fee the Catalan club paid for the 30-year-old.
But in an interview with the club's TV channel and website, Mathieu claimed he will be ideally suited to slot into the central defensive slot vacated by former Barcelona captain Carles Puyol, effectively arguing a younger player would struggle with the pressure.
"Being 30 gives you more tranquillity and experience when you talk to the press and deal with the atmosphere of big clubs," the Frenchman said.
"I'm very ready for the demands and pressure."
While Mathieu has played more of his career as a left-back, the former Sochaux and Toulouse man has almost exclusively lined up in the centre of defence over the past season-and-a-half with Valencia.
He is convinced he can succeed in that position with Barcelona.
"I will give 100 per cent of myself and I hope everything goes well on the pitch," Mathieu said.
"It's difficult to join a team after someone like Carles Puyol leaves but I will show Barca that they made a good choice in signing me."
In the past two seasons, Barcelona have lost two experienced centre-backs in Puyol and Eric Abidal, leaving the club with just Gerard Pique, Marc Bartra, Javier Mascherano and Alex Song as options in central defence - with the latter two more suited to defensive midfield.
Mathieu's arrival represents the first time Barcelona have gone out and bought a proper central defender since Dmytro Chygrynskiy arrived from Shakhtar Donetsk in August 2009.
Chygrynskiy played just 12 league games before being sold back to Shakhtar a season later.
