Saints meet the Premier League leaders after knocking out Fulham in the previous round.
A bullish Eckert said on Friday: "All of the pressure is on us, and it needs to be. If you want to win a game of football, the pressure is always on you, and it's for us to take that.
"We need to make sure we play a good game.
"The reality is that we go into a game to win, and we've always done that. For me, there is no other way. There is no other way that exists.
If you drop off that expectation and just put yourself in a role where you say, well, the pressure is on them, you only prepare yourself for bad results.
The pressure is on us, we want to win, and we'll do everything to do that."
On how he's planning for Arsenal, Eckert continued: "Well, it's a great team. I think rightfully every single manager in the press conference praises what Arsenal does, and I can only continue that.
"It's a fantastic team with many, many answers to problems. The preparation was fun, because it's just many more iterations of what you could do.
"You see that they do have answers to many possible solutions, but I think we have found a couple of bits that we're able to hurt them.
"We just need to make sure we bring that on the pitch."