Donny van de Beek's goal 15 minutes into the clash in north London was enough to give the Dutch side an advantage for the return leg in Amsterdam on May 8.
Erik ten Hag's side enjoyed a bright start but found themselves under pressure in the second half, and captain De Ligt was relieved to see out the victory.
“This is just one game but a very good starting position," he told Ziggo Sport. "The away goal is the most important. In the second half David [Neres] hit the post. Had the ball gone in, you would be sitting better. But we must be satisfied.
"You knew beforehand that it would be hard fought. We Dutch sometimes pretend Tottenham is some kind of B-team that we will walk over.
"Maybe it's better to go into a game as an underdog. We played well against Bayern Munich, Real Madrid and Juventus. Now you saw that Tottenham are good too. Then you have to fight and we have done that."
The 19-year-old added: "You know they are going to show something. With the long ball to [Fernando] Llorente, it was difficult to put pressure on them.
"We played well in the first half, they didn't touch it. After a while they started with the long ball, then we found it more difficult. We fought. It became a fight, but we stand here with the win."
Ajax midfielder Lasse Schone was also happy with the way his side limited the threat of Mauricio Pochettino's team, despite their struggle in the second period.
"We didn't play great after the break, but we didn't give away much to a good team," he said. "The team deserves compliments for this. We fought for every metre.
"They didn't get any really big chances in the second half either, they were mostly crosses. Moussa Sissoko did provide some dynamic, we had a hard time with that.
"At times we played very well. There was a lot of movement and that is how we created chances."