The Saints were able to beat lower league side Stoke City 3-2 in the Carabao Cup on Tuesday.
While the win is much needed, Martin knows that against better Premier League teams, his side will have to do more.
Speaking after the match, manager Martin said: "We spoke before the game about winning it and making sure we get through.
"I came back in and also saw Brentford with a really strong team out struggling against their Championship opposition - it's never easy in the cup.
"We got through, we made it tougher than it should have been for sure, but we also showed a bit of character to get through a bit of adversity in the game at 2-2.
"At 2-0, we conceded a goal which was madness because we were so dominant in the first half, I really enjoyed the performance.
"I think the final decision in the box in the final third wasn't quite there and we should have made more of the dominance we had," added Martin.
"At 2-1, the context of the game changes completely, so I was annoyed about that. Then we're trying to be aggressive and get caught on the counter-attack.
"Breezy scores and the defenders spent a lot of time in the opposition in the final third tonight because we were aggressive and we dominated territory."