Kevin Schade fired Brentford ahead shortly before the break, capping a first-half period in which Keith Andrews' side were comfortably the better team.
Farke's tactical changes shifted the momentum after the restart, and Calvert-Lewin eventually headed home to snatch a share of the points for the newly promoted hosts.
Andrews felt his side should have taken more from their first-half dominance.
"I thought first half we were magnificent. We got the lead and possibly could be more but we knew there would be changes. We couldn't play out through those chaotic stages. It shows where we are at that we are disappointed coming away from Elland Road with a draw," he said.
"We laid some really solid foundations last season that we want to build upon and it has been a good start to the season."
The Brentford boss was quick to credit his opponents' response.
"Never underestimate Daniel Farke - the way he sets up the team and the type of players Leeds have - they are very honest bunch. Slightly disappointing to come away with a point but we will probably look back on it and think it is a good point. We are growing all the time," Andrews said.
Farke, for his part, was full of praise for a Leeds United side he had asked plenty of during the match.
"I am proud of my players and I have to give them lots of compliments. We faced a red-hot form Brentford side," he said. "I asked a lot of them today, we changed formation for the second half, got control and lost control, changed the formation again and got the goal and pushed for the winner. A brilliant, excellent Brentford side and pleased to have reduced them to just one goal and we found a way back into the game."
The Leeds boss pointed to the value of in-game flexibility as his side continue adapting to life back in the Premier League.
"You can have an idea but all credit to the players to go and deliver that," he said. "To play a really good long season it is good for the confidence and good for the mood - we know we can be flexible and tweak things and change the formation even during the game a few times to find the solution. The players are buying in and ready to deliver. In the end it was a precious point."