The home side had an Alfredo Morelos goal disallowed and saw Bruno Alves' header cleared off the line.
Hearts struck the crossbar through John Souttar, but Caixinha was positive about Rangers' display.
"One team dominated from the beginning to the end," Caixinha told Rangers TV.
"I'm disappointed with the result, of course, which is the most important thing, but I really liked the team.
"[Hearts] tried to create something at the beginning of the game to delay our pace, they did it, but we finish the first half completely dominating, with some very good chances to score, which we could not do.
"I'm happy with the way they fought until the end.
"You cannot control this type of situation but what you can control is what the boys did, the effort, the hard work, the teamwork, not allowing the opponent to play and always looking to play our game."
Rangers have now dropped five points in consecutive home games - against Hearts and then Hibs - as Caixinha integrates the nine new players who arrived during the summer.
The Ibrox manager insists his side are playing well, but failing to convert chances and not maintaining a high enough intensity to their play.
"The only point I need to refer to is the pace of the passes needs to be higher, a higher tempo of passing and moving," Caixinha said.
"Regarding to the overall and especially the ending position on attack, we were very good.
"I don't remember one single transition from the opponent, or one single time where they could get the confidence to try to beat our last line.
"We did everything we could to win the game, we had the chances to win it but we could not do it.
"The timing and the tempo of the passes, the way we move in attack, yes definitely we need to improve that - that's all I take because the boys leave everything, they play the way we want them to play. We created chances and avoided the opponent having transitions, but we didn't score goals.
"We are controlling the moments of the game but should be more aggressive in the last third. To win you need to score goals, and we didn't do that."

Hamilton described the change as "too drastic" and the "worst-looking" modification in Formula 1 history.
John Surtees' son Henry died during a Formula Two race in 2009 after being struck on the head by a stray tyre.
"I suffered the tragedy of losing Henry which certainly could've been prevented by a development like this," he said.
Ferrari's Sebastian Vettel had said the device can be as "ugly as possible" as long as it helps save lives. The German also thinks Henry Surtees would "still be around if we had this type of system".
John Surtees, who won the 1964 drivers' championship with Ferrari, said: "Lewis could perhaps think a little more about the 'halo' and think about the responsibility he does have as a world champion.
"Change comes about and sometimes changes are forced upon one. It may be that the governing body, just because of the momentum and the fact that they have gone this way, will have no option but to impose these regulations.
"Henry was hit by a wheel that weighed 28kg so there would have been a chance there [had a 'halo' been installed]."
McLaren's Fernando Alonso, meanwhile, says the 'halo' device is a "necessary" step.
"It will be the future of F1, because we cannot afford any serious injury or fatal accident as we had in the last two years," said the two-time world champion, referring to the fatal injuries sustained by Jules Bianchi and Justin Wilson.
"I know the 'halo' is a little extreme in terms of aesthetics - maybe a canopy or other solution is found in the next couple of months - but hopefully next year we have one of these systems in all the cars."
Read more about the 'halo' here
Rangers manager Pedro Caixinha declared himself "happy" with Rangers' performance but "disappointed" with the outcome of the goalless draw with Hearts.
[NEXT_CONCEPT]
Lewis Hamilton has been urged to change his stance on the new 'halo' head protection device by former world champion John Surtees.