Spurs threw away three points at Goodison Park, conceding two goals in injury time as strikes from former player Steven Pienaar and Nikica Jelavic condemned them to a 2-1 defeat.
The 29-year-old, who missed the game due to injury, admitted is was extremely disappointing to lose in that manner but feels it must not let it affect their form when they host Swansea at White Hart Lane on Saturday.
"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.”
Despite the Swans' recent good run of results, bar their loss to Norwich, Dawson is confident his side can pick up a positive result at home.
"We will pick ourselves up and try to get back to winning ways back at White Hart Lane," he added. "We're confident we can beat anyone at home."