The hosting Swans were beaten 3-0 at the Liberty Stadium by the visiting Merseysiders, who controlled the contest throughout.
Looking ahead to future matches, veteran centre-back Tate has demanded that Swansea return to playing as a team rather than as individuals.
"It was disappointing, but that's what happens if you play as a group of individuals rather than as a team," Tate told the South Wales Evening Post. "We haven't got the players Everton have.
"We have gone away from the team aspect which made us good last season. We need to get back to playing as a team, otherwise we're going to struggle like that every week.
"If people are going to play individually we may as well pack up now."
The defeat has left Swansea 11th in the Premier League table.