Dawson, a January transfer window signing from Leyton Orient, felt he was at fault for failing to track Southampton goalscorer Adam Lallana, who went on to score both the Saints' goals.
"I'm honest and I came in at half-time and apologised to my team-mates and Flicker [assistant boss Dave Flitcroft]," Dawson told the club's official website.
"We'd worked really hard up until that point and I felt like I let the team down.
"I switched off and let him run by me. I've watched the game again and I can look back and see where I can improve.
"It's a learning curve for myself and you can't switch off for one second in this league because you'll get punished, but we showed bottle to try and play the right way."