Ronny Deila and Robbie Neilson both expressed frustration and admiration following a hugely competitive and dramatic draw at Tynecastle.
Celtic twice led, through Nir Bitton and Tom Rogic, with Deila praising "good spirit and high energy".
Hearts equalised through Sam Nicholson and Osman Sow, although Neilson said his players were "not happy".
"That's the mark of how far we be come, that there's disappointment after a 2-2 draw," the Hearts head coach said.
The Hearts goals came in stoppage-time in either half of a match that was relentless, full of determination and commitment.
Moments of composure were rare, but Celtic scored twice through accomplished touches from Bitton and Rogic.
Deila was also happy with the response his players showed to losing at home to Motherwell last weekend, a result that left the manager under pressure.
"I was very frustrated after last week, we were playing as individuals not as a team, and that was killing me inside," Deila told BBC Scotland.
"Today we fought together and showed spirit. Then sometimes we have to give credit to the opponent, it was an unbelievable goal [by Sow] but we will be hard to beat if we have that energy level.
"It was a big test for us, it was a very young team on the pitch and they responded very well.
"This has to be every time, that's top players and top teams, when they have that foundation of hard work and communication in the team. There were a lot of positives to take, but disappointing that we didn't win.
"It's tough, because I want to win and so do the players. My task is to give freedom to the players on the pitch and it's no problem for me to take the blame. If we play like that, we'll get a lot of points."
Neilson felt his players grew in confidence when they began to implement tactics they had worked on in training during the week.
That came after an opening spell that Celtic dominated without creating a clear chance. Neilson also insisted that while a top six finish remains the ambition for this season, Hearts can still challenge Aberdeen to finish in second place.
"It feels like a defeat because the way we played in first-half and the way that we can play, we should be winning those games," Neilson said.
"It was an entertaining game, it started frantically, and we lost a scrappy goal, but it was good to come back against Celtic twice. It shows how far we've come that the players are disappointed to take just one point from the game.
"We wanted to press certain players as quickly as we could and we caused them problems. We started to take control of the game, but it was tighter in the second half. We had to respect Celtic but also put them under pressure.
"The landscape changes quickly in this league. We have a game in hand that would move us to within touching distance of Aberdeen.
"We're getting close. Aberdeen are the aim and Celtic might be the aim in two or three years time."
Neilson also admitted that while Hearts are keen to sign Sow on an extended contract, they may struggle to keep the striker with his contract expiring at the end of the season.
"He's got that ability, he's a top class payer," Neilson said. "We'd like to keep him but there will be a lot of interest."
Deila revealed that Dedryck Boyata and Stuart Armstrong could be out for extended spells after both being injured and replaced in the opening half-hour at Tynecastle.
"Dedryck pulled his hamstring and Stuart had problems with his back, which he had in September as well," Deila said. "It will take some time for both of them."