Spurs led 1-0 in the 90th minute but the Toffees scored twice at the death to nick all three points to deny Dawson and his teammates the chance to remain fourth on the table.
But Dawson feels that disappointment can be used as motivation this weekend when Tottenham host Swansea City.
"It's always tough against Swansea, but we have to pick ourselves up after the Everton defeat," Dawson told the club's official website.
"We'd been on a brilliant run with brilliant performances and that was a little setback.
"We will pick ourselves up and try to get back to winning ways back at White Hart Lane. We're confident we can beat anyone at home."