Manager Joe Maddon said he enjoyed seeing the fans and their banners, which encouraged the team to finish strong until game No. 162.
Of course, Maddon's club did just that a year ago, overcoming a big deficit in the standings to overtake the collapsing Red Sox on the last day of the regular season to win the American League Wild Card.
"We just have to believe that we can do this," Maddon said. "We've got to come out and we've got to prove it. We've got to do it nightly. We have to have a short memory."
The Rays entered Monday's game vs. the Red Sox five games behind the AL East-leading Yankees and four back in the AL Wild Card standings to another division rival, the Orioles.
Maddon maintained that his team is still not out of the race and said the Rays need to take advantage of the opportunity when it presents itself.
"Just like we stubbed our toe last week, somebody can do the same thing this week," Maddon said. "We have to be in a position to take advantage of that toe stubbing."
Though Tampa Bay concluded its season series with New York on Sunday, the Rays will play one more series against Baltimore from Oct. 1-3, the last series of the year that could again decide its fate.