Goals from Christian Eriksen and Dele Alli put Spurs in control at the break but Mauricio Pochettino's side struggled to repeat such early domination during the second half.
James Ward-Prowse's strike set up a nervous finale but the north Londoners hung on to their advantage and cut Chelsea's lead at the top of the table to 10 points.
Spurs have had to see out games against the Saints and Everton in difficult circumstances in recent weeks and Janssen is adamant doing so is testament to the resilience Pochettino's players possess.
"They are a good team so we had to keep hold of the three points and that’s what we did at the end," Janssen told Tottenham's official website.
"Mentality is very important and we are a very strong team mentally - you can see that.”
Spurs have long been accused of possessing a soft underbelly but Eriksen is convinced he and his teammates have learned some valuable lessons in regards to seeing games out.
"In the second half it was a different game. We showed we’ve matured from last season where we only conceded one goal, not two when we’re 2-0 up,” said the Denmark international.
Meanwhile, Spurs have 13 days without a game and will travel to Burnley following the conclusion of the international break.