Spurs are in fifth place in the Premier League following Sunday's 1-0 victory over Cardiff, but face Chelsea, Arsenal, Southampton and Liverpool this month.
Vertonghen, who has previously hinted that he may quit White Hart Lane if Spurs fail to secure UEFA Champions League football next season, knows they will have to play better than they did against the Bluebirds.
"We needed those three points, but we will have to improve because we are playing better sides in March," the 26-year-old said.
"It is not just Liverpool we are chasing; I think there are other teams who can drop down. We are just watching fourth place - it does not matter who we catch.
"It was not our best game (on Sunday) but we are back on track after losing to Norwich."
Tottenham take on leaders Chelsea at Stamford Bridge on Saturday, live on Sky Sports 1HD, with 10 points separating the London clubs in the standings.
Vertonghen is braced for a battle against international team-mate Eden Hazard this weekend, but acknowledged Chelsea boast plenty of other threats too.
"He is in good form and we will need to defend well against him," Vertonghen said.
"But it is not only Hazard. Andre Schurrle scored three times against Fulham, they have midfielders who can score goals and they are strong from set-plays.
"It will be an important game for both of us and we want a good result."
Roberto Soldado scored just his second Premier League goal in open play for Spurs against Cardiff - and his first of any kind in two months. And Vertonghen hopes the strike will kick-start his career in England.
"It was a good goal and he needed that," he said. "He is doing a lot of work for us without scoring goals but for himself, for the press and for everyone, it is good that he scored a goal to take the pressure off.
"Everyone saw the celebrations with him after the goal. We all like him and we are all very happy for him."