Spurs were outplayed at times by the hosts.
"There is no hiding the disappointment when you come here and lose," Dawson told the club's website.
"We know what it means to everyone and it's a tough one to take.
"We had a real go and we were hoping something might just fall for us. The goalkeeper made a great save from Jermain and we just needed a little luck. It wasn't to be.
"We have to move on. Football can be a cruel game and it will be a frustrating couple of weeks now until the game against Norwich.
"We've a while to stew over it, but we have the chance to put it right and I'm sure the fans - who were fantastic at Arsenal - will be back at the Lane as we try to do that."
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