Ahead of the game, Janssen had failed to net in his one previous start and five substitute appearances since making the summer switch from AZ Alkmaar, but the Netherlands international converted from the penalty spot in the 5-0 win at White Hart Lane.
With Harry Kane sidelined for the foreseeable future, Janssen will become the first-choice forward at the club, and Pochettino is confident that his new signing will add to his tally in the coming weeks.
The 44-year-old is quoted by BBC Sport as saying: "Now that Harry Kane's injured Janssen is our main striker and it's important for his confidence for the next few games.
"That goal was important for him, to feel the love from the supporters. For a striker, always the difficult thing is to create chances but he has a lot of chances to score today. He was unlucky.
"The important thing is that he got into the box and he created a lot of chances and for the future it's important that he feels confidence and for the team it will help a lot for us."
Spurs' reward for beating Gillingham is a last-16 tie away at Liverpool.