The holders won 2-0 thanks to goals from Fabian Schar and Nick Woltemade.
Frank said, "I think it was a very even game. I think it was small margins that decided it. I think our performance was good. I think the way we played the game, especially how we built it from behind, phase one, especially phase two, I think we controlled the game much more. I think we had some short connections in the middle of the pitch. I think we found Lucas (Bergvall) and Xavi (Simons) in good positions.
"So I think it was one of our better offensive performances for the season. You could say it was not like we created five hundred percent chances, but we created some really big chances.
"I think (Newcastle keeper Aaron) Ramsdale had some really good saves. And then I think we had six, seven very good moments where with Richarlison arriving half a second too late, the final pass could have had even more cutting edge quality to have created even more.
"So overall, I'm happy with the performance. Of course, I'm super disappointed that we lost. And I'm super disappointed that we're out. We would love to progress and be in the draw tonight."
On his team selection, Frank also said: "It was very difficult, to be honest. You said that Newcastle made eight changes, we made four. But I think we made four because we wanted to compete and I think we competed. Unfortunately, we just dropped out on the wrong end of it. So, of course, as you say, it's a busy schedule.
"It's a balance to make a very competitive team that can perform and tactically still hit the criteria we want to hit. We played Everton, four changes, Newcastle four changes and then Chelsea on Saturday.
"Some you need to rest, others you need to be able to perform. So, of course, I'm very disappointed we couldn't continue. I think we have 5,000 fans travelling. So we're more than pleased, happy that they're travelling this long way on a late night and give us all the backings. Unfortunately, we couldn't give them back a win."