The Belgium defender last week indicated he may look to leave White Hart Lane in the summer if Tim Sherwood's side do not secure a place in Europe's premier club competition next season.
Sunday's 1-0 victory over Cardiff at White Hart Lane consolidated fifth place in the Barclays Premier League, and Spurs now face Chelsea, Arsenal, Southampton and Liverpool in a pivotal March schedule which Vertonghen believes will make or break their European ambitions.
"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."
Liverpool are rumoured to be monitoring Vertonghen's situation, poised to pounce should the former Ajax defender make good on his Champions League threat should Tottenham miss out.
Spurs trail fourth-placed Manchester City by four points, but Manuel Pellegrini's men have two games in hand over their title-chasing rivals.
Tottenham take on leaders Chelsea at Stamford Bridge on Saturday, 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 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 broke his two-month goal drought in Sunday's win over Cardiff, and Vertonghen reckons the pressure-release could fire the Spain striker into top form.
"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."