The Cherries won 1-0 in London thanks to Evanilson's early goal.
Frank said afterwards: "We clearly didn’t perform well today. We played against a very good Bournemouth team that we know can make it difficult for any team in the league. They played to their strengths.
"They did that very well and we didn’t handle it well. We knew exactly what they came with and we trained for it. We just didn’t handle it well enough in terms of the balls in behind, the second balls, duels in the middle of the park.
"That’s the defensive side and on the offensive side we struggled to find good enough solutions to get through phase one and two so we could get up there and put a bit of pressure on them. We only did that in the last 15 where we put on good pressure and could have equalised. I think over the game it was fair that Bournemouth won."
Spurs players were booed off at halftime and at the final whistle by the home support, something Frank hopes will be rare this season.
He also said, "I prefer them not to boo, but I understand. It was not a good performance today and they have high expectations, which is absolutely fair.
"I think let's say if we perform even better and still lose the football match today, I don't think we hit the level we should. I think the players gave everything and then that's the foundation and put the heart out there, but football wise we didn't hit our top level today."