Tottenham Hotspur drew 1-1 with their Merseyside counterparts on Saturday.
The 22-year-old striker started on the bench but came on and impressed after Mauricio Pochettino introduced him with over half-an-hour to go.
The Netherlands international, a £17 million signing from AZ Alkmaar, looked certain to score what might have been the winner at Goodison Park, but Toffees goalkeeper Maarten Stekelenburg pulled off a fine save to keep him out.
Janssen has now admitted to the club's official website that he thought he had scored in that moment, and concedes that he was disappointed not to have experienced a goalscoring feeling on his Tottenham bow.
“I thought I’d scored. I thought it was a goal. That’s why my own feeling is a little sad - it could have been a fantastic moment.
"It still was a fantastic moment for me to play my first minutes for this club but it would have been even more if I could have scored one.”
Despite not scoring, Janssen did more than enough to convince Spurs fans that he can be a big player for them this season.
With a Champions League campaign on the horizon, Tottenham will have to rest Harry Kane - last season's top goalscorer in the Premier League - at times, and Janssen's performance at the weekend has prompted optimism that he can be an able deputy.