De Boer's men created a big chance with the scores all level at Anfield, which Christian Benteke failed to take on his return to Merseyside, and that would come back to haunt them as Sadio Mane prodded home a 73rd-minute winner.
"I think we played almost 90 minutes very concentrated, very solid. Of course we played deeper than we'd normally want, but we know the opponent we face today," the Dutchman told reporters after the match. "We tried to create chances, and I think we did, I think we frustrated Liverpool sometimes because we were very organised and disciplined.
"I think we were very concentrated, and one unlucky touch from Luka [Milivojevic] we conceded the goal. That's a pity, but I said to my players if we show this spirit every week I am confident. I'm happy with the spirit, not happy with the result, but I think we can build from here. We played as a team, that's what I saw today, and it gives me hope for the future."
De Boer becomes just the second Dutch manager to lose his opening two Premier League games after Martin Jol, who suffered three in a row during his time at Tottenham Hotspur.