Magpies striker Alexander Isak opened the scoring just before halftime at St James’ Park after side-footing home Jacob Murphy’s cross.
The Bees equalised midway through the second half after Bryan Mbeumo converted from the spot for his 16th goal of the season following a Nick Pope foul on Yoane Wissa.
The winning goal came from Newcastle’s Sandro Tonali after 74 minutes when the Italian’s cross-come-shot flew into Mark Flekken’s goal via the near post.
And for Frank, he recognised it was a game that could have gone either way.
"I'm very happy with the performance overall," he said. "It was a performance that easily could have given us three points again.
“I think that was a brilliant away performance in the first half. In the second half, we are coming back into the game.
“So, the performance is very good.
“But to win a tight game against a good team, you need some of the margins to go your way. And the first goal, Bryan slips. If he does not slip, he kicks the ball away in front of Isak.
"They embraced the atmosphere, they enjoyed playing in it. We were brave, we were aggressive. It \[St James’ Park\] is a difficult place to play.”
Brentford had their own chances to take the lead when the game was level – Ethan Pinnock’s header hitting the post – and to equalise when they were trailing, as Kevin Schade and substitute Mikkel Damsgaard saw their efforts fail to find the back of the net.
The Dane explained that sometimes football is a game of fine margins and was keen to speak to Tonali after the game to find out whether he meant his goal.
He added: "We had Ethan's header which hit the inside of the post, then Tonali scores from a cross which is one in a million. I even asked him after, and he said it was a cross!”
Brentford’s goal scorer Mbeumo also thought the performance of his side was good but was left frustrated at leaving the north east with no points.
Speaking post-match, he said: “It was a good performance but at the end it was not enough. I think we knew it was going to be a tough game against a very good side and at the end it was a bit frustrating. It is hard to take.
"We knew it is important to get the points away. It is always tough to come here. It is really tight, and we are going to give it our best game by game and see where it takes us."
The result ended a run of five-consecutive away league victories for the London-based team and leaves them 11th in the Premier League, eight points off Chelsea in sixth place.
Frank’s team will now turn their attention to the Blues as a West London derby with Enzo Maresca’s team awaits on Sunday.