The Spurs head coach insisted there were clear signs of progress in his team's defensive work.
The result means Brentford are in 9th position in the Premier League standings, while Tottenham are in 12th position.
Frank was booed by sections of the travelling support at full-time at the Gtech Community Stadium as he led his players towards the away end. The reaction followed a flat attacking display in which Tottenham managed just two shots on target and failed to build on their recent win over Crystal Palace.
Speaking after the match, Frank accepted the criticism aimed at his side's lack of cutting edge, but stressed that the clean sheet deserved recognition.
"I think they seemed like they were not too satisfied, and it's fair," Frank said. "When we don't hit a top performance overall, that's understandable. But it's double-sided because we also need to acknowledge the defensive side of the game.
"We were excellent defensively today against a team that just scored three against Liverpool, three against Manchester United, and so on."
Tottenham recorded a second consecutive away clean sheet, something Frank believes reflects important progress after a difficult period.
"Of course, the offensive part needs to be better. There's no two ways about that," he added. "You prefer everyone is happy and we are winning three-nil. But it's about understanding where we are right now as a team and as a club."
Frank has faced growing scrutiny over his approach since taking charge in June, with some fans calling for a more attacking style. However, the Dane insisted the current balance is a response to the team's situation rather than a lack of ambition.
"It's not that we don't want to play attacking football," he said. "When you are not at the top of your game and you struggle to score goals or create enough chances, you can't open up too much. If you do, you need to score too many goals. It's a fine balance."
Arne Slot has admitted Liverpool may have missed a key moment after Hugo Ekitike stayed on his feet instead of going down under pressure, as Leeds held the Reds to a 0-0 draw at Anfield.
Pep Guardiola admitted his frustration after Manchester City failed to turn dominance into goals and were held to a 0-0 draw by Sunderland at the Stadium of Light on Thursday.
Liverpool's momentum stuttered on New Year's Day as they were held to a 0-0 Premier League draw by Leeds United at Anfield.
Enzo Maresca has left his role as head coach of Chelsea after 18 months in charge at Stamford Bridge, the club confirmed on New Year's Day.
