Mark Warburton's men's five-game unbeaten run was ended by Robbie Neilson's side as Robbie Muirhead scored either side of half-time to send the Jambos into second in the Scottish Premiership table, with the Gers dropping to third.
Rangers' Kenny Miller
And Miller has conceded that the better team won on the night.
"We've lost three games away from home to three good teams this season. So we've had to adjust to the step-up to this league and you could say that we’re still adjusting," he said, as reported by the Evening Times.
"But we are getting used to it. Hearts are a decent team at home and we weren't good enough. Simple as that. We never really created much.
Rangers manager Mark Warburton
"The offside decision is maybe a big turning point as we never played at all. We weren't great. But if you get that then maybe it turns for you. But overall tonight we weren't good enough and can have no complaints."
Although it was always going to be a tough ask to go to Hearts and pick up a victory, Rangers supporters will have surely come away from the game with a huge sense of frustration.
Their recent victories over Dundee and Partick Thistle were perhaps not pretty, but they hinted that the Light Blues had turned a corner as they found a way to win even though they were drawing going into the dying minutes in both games.
Rangers face Aberdeen at Ibrox on Saturday
However, this latest loss arguably suggests that they have done little to address the inconsistency that has prevented them from putting three consecutive wins together in the top flight this term.
And that frustration may perhaps move to another level if they lose at home to Aberdeen at the weekend, especially as they are already vulnerable to falling behind the Dons in the table, with only a two point advantage over Derek McInnes' men even after playing two games more.