The Austrian, who was one of the best players on the park at Easter Road, admitted it was “sore” to concede so late to Martin Boyle but felt there were big positives to take from the performance.
Despite defeating Ross County on the opening weekend, Hearts were better against their rivals.
They had numerous chances to finish the game off after the break but were thwarted by last-ditch defending, wayward finishing or strong goalkeeping.
“It was a sore one to take after the game obviously, and even the day after,” Haring said. “But looking at the bigger picture and at the performances, it might sound a bit strange, but I personally felt better after Sunday’s game than after the first weekend.
“Even though we won that first game against Ross County, I think we played nowhere near the levels we can.
“Last weekend was a much better performance, but we lost the goal in the last seconds of the game.
“We know we could have done better. We’ve looked at it and we know what we should have done differently.
“But the overall performance was much more pleasing last weekend compared to the first game.”
Haring has been enthused by what he has seen of the new look attacking quartet. Barrie McKay and Liam Boyce have been joined by new boys Alan Forrest and Lawrence Shankland.
Forrest and McKay were on the scoresheet against County, while the latter set up Shankland for the opener in the derby.
The view at Hearts is that as long as they keep it tight at the back they will win games with so much threat and quality in the final third.
“We’ve got loads of quality up front,” Haring said. “We’ve got that everywhere but I think we’ve got more depth up front this season than we had last season.
“Every player in our squad is capable of scoring goals, so the chances are quite high if we don’t concede that we’re going to win the game.”