Steven Thompson put the Buddies head of just three minutes at St Mirren Park, but profligacy from the home side proved costly when Jamie Hamill scored with a volley to level the game.
Lennon was also frustrated St Mirren were denied a penalty when Brad McKay appeared to handle a Jim Goodwin shot shortly after Hearts squared the match.
"It was a terrific start for us. We kept the momentum going and we created good opportunities," Lennon said.
"The only thing we didn't have in the first half was another goal. We warned them at half-time that Hearts would come here and fight for every single point.
"That showed in their five yellow cards compared to none for us. I'm in no way saying it was a dirty game; it just showed how committed they are to fighting for every point.
"I thought we could have had a stonewall penalty but I felt at times some of the players lost that focus.
"It's a game where two valuable points have been dropped in terms of where we want to be."
Hearts counterpart Gary Locke claimed he feared the worst when Steven Thompson pounced to net the early goal.
Locke said: "It was a poor goal. We had a couple of chances to clear it and we didn't and Thompson scored.
"But I thought we reacted in the right manner and we got ourselves back in the game.
"There wasn't a lot in the first half but we were dominant in the second half and very unlucky not to get three points."