Arsene Wenger's side have lost their last two matches, against Dinamo Zagreb in the Champions League and Chelsea in the Premier League.
The club have not lifted the League Cup since 1993 - when Seaman was in goal - with two runs to the final in the past nine years ending in defeat in the showpiece.
And Seaman believes that the Gunners simply must progress to the fourth round, and has subsequenly called on Wenger to name a strong side to face Mauricio Pochettino's team.
"Arsenal's start has been okay, but it's not been as good as what they hoped for I'm sure," Seaman said.
"They have not had a great start, then they had a few good wins but they are going into this game off two defeats, and they don't want to go into their next Premier League game after three defeats.
"So makes it a little bit more important for Arsenal to win in that aspect. It's a massive game for the players and even bigger for the fans, the bragging rights are obviously dictated by who wins.
"It will be a good game, and will be interesting to see what sort of side both teams put out because they will definitely put some not regular first teamers in there.
"It is important both put decent sides out there because if Tottenham put a full strength team out and Arsenal put a youth team out it's not a good challenge. It's about getting the mixture right."