Matthijs de Ligt's header at the death denied Spurs a chance to move into second place in the Premier League, at least until Sunderland host leaders Arsenal, but Frank said a significantly improved performance after halftime had pleased him.
Spurs' home form in the league remains a concern, though, with five points from six matches and only a single win, which came against newly promoted Burnley on the season's opening day.
Some fans made their displeasure known at half-time with boos, which also greeted Frank's decision to replace the lively Xavi Simons with Mathys Tel, though the change proved to be inspired.
Tel levelled the game at 1-1 and sparked the turnaround, finishing after a move down the left involving two other substitutes, Wilson Odobert and Destiny Udogie.
Seeking 'right balance'
Frank's efforts to add defensive solidity to Spurs have left them looking short of ideas up front, though they were better in the second half.
"We're playing at home. Of course, we all want to win and, you know, don't talk too much about home form and all that – and I know we need to win before we don't talk about it," he said.
"But the way we turned around to stay in the game, kept doing the right thing throughout the second half, very, very happy with that – and also so close to winning it. And, on any other day, we win it."
Frank conceded that Spurs were "searching to find the right balance up front" after PSG loanee Randal Kolo Muani was substituted at halftime following an anonymous display. But he also pointed to a good chance missed by Richarlison when the game was at 0-0.
"One of the biggest chances was Richarlison from a cross from Brennan (Johnson)... (if) he scores on that instead of Bryan (Mbuemo), it changes a little bit and opens up the game a tiny bit more," Frank said.
"But we constantly work on the relationship and try to improve with the players and try to find what is exactly the right plan, but I think there were small steps in the right direction."