Newcastle celebrated the Cup with fans on Saturday in an open-top bus parade through the city.
Howe addressed supporters, stating: "You can’t help but see from that bus what it means to represent this football club. We need to take that seriously and continue to do so from this day forward - and try to bring more moments like this for the people.
"We are hungry for more. But we can’t get ahead of ourselves. We have 10 huge Premier League games to go back to and try to qualify for the Champions League. But the taste for success leaves you wanting more days like this.
"There are two ways we can react to this cup win. We have to take the positive, not the negative. We have to use the love and feeling that we got today as a driver to work harder, train harder - and our focus from today is very much on the future."