Rodriguez, who hit .332 with 35 homers and 113 RBIs, finished with seven first-place votes and 252 points in balloting by the Baseball Writers' Association of America.
"That's the dream of every player, to get this award," Rodriguez said.
Martinez, who won the AL Cy Young Award earlier this week after going 23-4 with a 2.07 ERA and 313 strikeouts, had eight first-place votes and 239 points.
"It's fine. It's fine. I'm not going to cry about it. It would have been a great honor," Martinez said. "I got the Cy Young. That's good enough."
Ivan Rodriguez became only the fourth MVP to win without getting the most first-place votes, joining Detroit's Hal Newhouser, who beat teammate Dizzy Trout 236-232 in 1944; the New York Yankees' Roger Maris, who beat teammate Mickey Mantle 225-222 in 1960; and Pittsburgh's Roberto Clemente, who beat Los Angeles' Sandy Koufax 218-205 in 1966.
Rodriguez said he would have picked himself first, Martinez second and Alomar third. He said he didn't agree with those who say pitchers shouldn't be eligible.
"I think the MVP should be for everybody," he said.
Voters list their top 10, and Rodriguez won largely because he was listed on the ballots of all 28 voters while Martinez was not listed by two: George King of the New York Post and La Velle Neal of the Minneapolis Star Tribune.
In 1947, Boston's Ted Williams lost the MVP to the Yankees' Joe DiMaggio 202-201 despite winning the Triple Crown because Boston Globe writer Mel Webb, who did not like the sometimes-surly Red Sox star, left Williams off his ballot.
Rodriguez received six seconds, seven thirds, five fifths, two sixths and one seventh, while Martinez got six seconds, four thirds, one fourth, two fifths, two sixths and three sevenths.
Rangers designated hitter Rafael Palmeiro was fifth with four first-place votes and 193 points, and Yankees shortstop Derek Jeter was sixth with one first-place vote and 177 points. Boston shortstop Nomar Garciaparra was seventh with 137 points.
"Everybody that was in the pile was good enough to be MVP so I don't hold anything against anybody," Martinez said. "There's nothing I can do. If they don't want to vote, it's up to them."
First-place votes are worth 14 points, seconds are worth 9, thirds worth 8 and so on.
Texas players have won the award in three of the past four years. Gonzalez, who was traded to Detroit earlier this month, won in 1996 and '98. The Rangers' only other winner was Jeff Burroughs in 1974.
Rodriguez's batting average was the highest by an AL catcher since the Yankees' Bill Dickey hit .362 in 1936. Rodriguez also became the first AL catcher to hit .300 and reach 100 in runs (116) and RBIs. He threw out 39 of 72 runners trying to steal (54 percent).
Martinez, a unanimous Cy Young winner, had hoped to join Denny McLain (1968), Vida Blue (1971), Rollie Fingers (1981), Willie Hernandez (1984), Roger Clemens (1986) and Dennis Eckersley (1992) as the only AL pitchers to win the Cy Young Award and MVP in the same season.
Don Newcombe (1956), Koufax (1963) and Bob Gibson (1968) did it in the National League.
"It would mean a lot, probably more than this Cy Young alone," Martinez said Tuesday. "I've already achieved that, so the MVP would be something different, especially to a pitcher."
Ramirez's 165 RBIs were the highest single-season total since Boston's Jimmie Foxx drove in 175 in 1938.
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