A 1-0 defeat coupled with an abject performance saw the Spurs players jeered from the field at White Hart Lane as Wigan became the latest team to test Andre Villas-Boas' side on home turf.
Belgium international Vertonghen now expects a response from the players in a week where they face Maribor in the Europa League before travelling to face Premier League champions Manchester City on Sunday.
"The team is strong enough to come back from this defeat," he told the club's official website.
"We have a lot of important games ahead, important games in Europe and difficult away games.
"We have to stick together. We know we're strong in away games and we can win at any away ground."
Ben Watson's second-half winner for Wigan means Spurs have taken just six points from a possible 18 at home in the league so far, losing to London rivals Chelsea and being held by West Brom and Norwich.
Vertonghen highlighted Wigan's formation as a reason for the unexpected loss and felt it was a missed opportunity to get some important points on the board.
"We had problems with their system, but normally we turn it around," he said.
"We just couldn't do it and it was a shame for the fans because it was a big opportunity with Arsenal losing, plus Fulham and Everton drawing. Overall, it was very disappointing."