Martinez was hotly-tipped for the vacant managerial hotseats at Aston Villa, Liverpool and then Tottenham Hotspur ahead of Andre Villas-Boas' appointment, but will take charge of Latics for a fourth season in the top-flight.
"The players have been in the same boat as the fans over the past few weeks, keeping up to date via the papers and Sky Sports News," Pollitt told the Wigan Evening Post.
"It looked like it was all right for a few weeks, and then when Harry Redknapp left Tottenham I thought: Oh no.
"It has been a bit unsettling these last few weeks, not really knowing what's been going on with the manager.
"But we're all delighted he's staying, and let's hope he can keep us moving up that table."