The Bees were comfortable 3-1 winners via Bryan Mbeumo (2) and Yoane Wissa's goals. Yukinari Sugawara struck an impressive consolation for Saints.
Martin later said: "We're very disappointed with the result and the goals we conceded. I feel like we're hurting ourselves a little bit. We had the best chance in the first half with Adam Armstrong. it's about taking a breath in that moment, that's my job to get rid of the tension. I don't think there was much in it between the two teams. We have to stop making mistakes that hurt us.
"What comes first is us and I don't think Thomas (Frank) will say it's their pressing because it's mistakes from us. We get punished in the Premier League as you do in the Championship. it's a much better performance than against Nottingham Forest.
"The subs had a great impact and the team will be different against Manchester United, that is for sure. Cam Archer was great when he came on. Adam Lallana came on and showed you how much quality he has.
"It's a brilliant goal but we should have scored two or three today."