Eto'o, who joined the club on a Bosman in August, starred in the Toffees' 3-1 win over Burnley on Sunday by bagging a brace, with his second goal particularly impressive.
In contrast to that free transfer, Martinez signed Romelu Lukaku for a club-record £28m in July, and Baines says that the 21-year-old Belgian will learn plenty from the veteran hitman.
"It was a great signing, and for us to pull that off and bring him in is great," he told The Express. "He gets the goals that win us games, and who better for Romelu Lukaku to be learning off as well?
"Obviously we spent big money on Rom. So in terms of finance we put all our eggs in one basket and then to so come up with a free one like Sam is brilliant.
"He's such a good player that it was never going to take him too long to settle. He used to be about pace and power and now you see his awareness of how to being other players into the game. But he's still a great finisher so he's a really good fit for us."
The 33-year-old former Cameroon international, who spent last season with Chelsea, signed a two-year deal at Goodison Park.