After all, doing so would prove quite an achievement for Toronto, given that the last time it finished ahead of New York was 1993, the same year the Jays won their second consecutive World Series.
Gaston reiterated his stance prior to Tuesday's opener of a three-game set against the Yankees.
"Third place is certainly better than fourth place," Gaston said. "To finish third is very important for us. We're going to see if we can go out there and hopefully finish third."
The Jays took a step in the wrong direction on Tuesday though, as they dropped a 3-1 affair to the Yankees at Rogers Centre. With the loss, fourth-place Toronto now sits three games behind New York in the AL East standings.
The Jays couldn't make use of a strong outing from starter Jesse Litsch in Tuesday's contest, as they couldn't provide him with much run support.
Litsch, who suffered his first loss since Aug. 28, held the Yankees to just three runs -- two earned -- on five hits over his seven innings. The right-hander walked one while striking out a career-high eight batters.
Litsch's strong performance was nothing new, as the 23-year-old has dominated hitters since returning from a stint in Triple-A Syracuse, where he spent three starts retooling his pitching arsenal. Upon his recall, Litsch has posted a 2.00 ERA over his eight starts. During that span, he has allowed just 41 hits over 54 innings.
The only negative is that his hot streak has come just as the 2008 campaign is in its final days.
"It's definitely tough, but that's just something to build on for next year," Litsch said. "You finish strong and come into next year with the same attitude that I've had in the past six or seven starts. It's what I'm going for right now. It's something to build on. We're not in a race so you have to think about next year in the same regards."
On Tuesday, Yankees first baseman Jason Giambi reached base in the second inning with a single off Litsch, and then scored New York's first run when Robinson Cano grounded out to second base. Giambi again factored in the scoring in the fourth inning, when he launched a 2-2 offering from the Toronto starter into the right-center field stands for a solo home run -- his 32nd of the season.
The Yankees completed the scoring off Litsch in the seventh, when Robinson Cano doubled and advanced to third base on a wild pitch. Cano then proceeded to score on a passed ball that catcher Gregg Zaun couldn't handle, giving New York a 3-0 lead.
The Jays' offense didn't muster much against New York's pitching. Right-hander Mike Mussina started the game for the Yankees and pitched five shutout innings to collect the win. With the victory, Mussina reached the 19-win plateau for the third time in his career and first time since 1996.
Mussina was followed by five Yankee relievers, who combined to preserve the lead. Scott Rolen's seventh-inning RBI single amounted to the Jays' only run.
The problem for the Jays' offense in the loss proved to be strikeouts, as Toronto's hitters whiffed a season-high 14 times.
"That's a lot of strikeouts," said Gaston, flatly.
The strikeouts also came at the worst possible times for the Jays. On two occasions late in the game, Toronto was able to put the tying runs on second base, yet could not convert. Yankees reliever Joba Chamberlain escaped the seventh inning by striking out rookie Travis Snider, and then ended an eighth-inning threat by punching out Lyle Overbay.
Gaston noted that many of his players were complaining about home-plate umpire Larry Vanover's strike zone.
"It seemed like the balls were off the plate," said Overbay. "Scott Rolen said it best, 'When you're protecting [the strike zone] at 0-0 in the count, it's tough.'"
Litsch wasn't complaining though, as he was able to set a new career high for strikeouts in a game.
"It goes both ways," Litsch said. "It's a pitchers and hitters game. Sometimes you're getting balls off the plate and sometime you're not. I'm not really in tune to what they were getting but I felt fine with it.
"It's just one of those games where it goes that way."
David Singh is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.