The Foxes largely dominated at the King Power Stadium and were cruising at 2-0 with less than half an hour left thanks to goals in either half from Thomas Castagne and Kiernan Dewsbury-Hall.
Ivan Toney sparked Brentford's unlikely fightback by reducing the deficit in the 62nd minute before Dasilva's stunning 86th-minute thunderbolt.
Frank said: "Such a big credit to the players' mentality. This group of players, just wow!
"A lot of teams would have broken down and not got back into the game, but we were running so hard.
"I think we looked fit. We were on top at the end of the game and then of course there's a fairytale story for Josh Dasilva, being out for 18 months.
"So pleased with a lot of things, but a lot of things to work on."
Frank said it was a landmark moment for the Bees midfielder Dasilva, who returned to action in February having been sidelined for 18 months due to a career-threatening hip problem followed by a hamstring injury.
Frank added: "When he first scored I'm just very happy of course for the equaliser because every point in the Premier League you have to fight so hard for.
"But after the game in the dressing room I thought about Josh and I wanted to say some nice words to him.
"It was emotional because he's been out for 18 months, he's a player and a person I've worked with for four years. He's a fantastic person.
"Seeing him coming back to the level we know, producing that top moment which also gave us a point, was very emotional and I'm very pleased for him."