First-place votes were worth 3 points, second-place votes 2 and third-place votes 1.
Lamont received 8 first-place votes, 9 second-place votes and 5 third-place votes.
"When the season started, I said he had no chance, but now I think he'll get a lot of second- or third-place votes," Cook said.
He finished third in the American League Rookie of the Year voting with 1 second-place vote and 11 third-place votes.
Pujols, the feared hitter with the St. Louis Cardinals, received 12 firsts, 19 seconds and one third-place vote for 347 points.
Each voter selects first, second, and third-place votes.
He garnered 25 first-place votes, 84 second-place votes, and 182 third-place votes.
Fields received one third-place vote for AL Rookie of the Year.
Yankees closer Mariano Rivera finished third in the balloting, with one second-place vote and 24 third-place votes.
But Miami was third on two ballots compared to one third-place vote for Washington.
