Ajax won their first trophy of the season on Sunday with a 4-0 victory over Willem II at De Kuip, with goals from Daley Blind and Rasmus Kristensen either side of a Klaas-Jan Huntelaar brace ending a five-year silverware drought.
They remain well in the hunt for a treble, with Ten Hag's side leading the way in the Eredivisie due to their superior goal difference over defending champions PSV, while they are 1-0 up halfway through a Champions League semi-final against Tottenham.
And ahead of Wednesday's return against Spurs at the Johan Cruyff ArenA, Ten Hag insisted Ajax will not be satisfied if they do not go on to achieve more success this campaign.
"In the end, it's all about titles," he told reporters.
"We have been fighting for this all year round and the first prize has now arrived. But we are not yet satisfied. It is not enough.
"This fuels hunger. Now we are going to enjoy it for 24 hours, but after that, the focus will be on Wednesday.
"It has been far too long since Ajax had won something. We have had a great season, but we needed something tangible. We now have that, but we want more.
"We have fought hard and I was very happy to win this trophy for the fans because they had long to wait."
Though Ten Hag was adamant Ajax cannot be content with just one trophy, he added that the KNVB Beker win - Ajax's first in the competition since 2010 - will enhance their confidence.
"This was the ideal scenario, this win gives us a boost," he said.
"It is wonderful to work with this team. They radiate so much pleasure. During the competition but also after the final when they celebrate with the supporters. I can really enjoy that."
Ajax defender Blind echoed Ten Hag's thoughts.
"I had not won this prize yet. Twice I played the final with Ajax, but twice it went wrong," the former Manchester United man told reporters.
"I really wanted to win this cup. It is wonderful that we have now succeeded. We needed this competition as ideal preparation for Wednesday.
"We craved a trophy. This is the first, hopefully, more will follow."