Janmaat was making his debut for the club following his move from Feyenoord last month, and he believes that they played well enough to earn at least a draw.
"We are disappointed because we felt we deserved more than this," he told Newcastle's official website. "It's a shame that we didn't at least get a point, especially with the way we played in the second half. We had a lot of good chances but you have to score one, and we didn't do that.
"There were lots of positives to take from the game and we have to take them on board now and move forward.
"When you can play like that against the champions, you know you have done something right. But that is why we are so disappointed - because we played so well."
Newcastle will return to action with a trip away to Aston Villa in the Premier League next Saturday.