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The former Ibrox loanee believes Rangers had the players capable of delivering the championship under Danny Rohl but crumbled when the pressure intensified.
Speaking to Record Sport, Moore reflected on how Rangers went into the Premiership split knowing five victories would be enough to secure the title after recovering from a 13-point deficit earlier in the campaign.
However, defeats to Motherwell, Hearts, Celtic and Hibernian saw their hopes unravel as they eventually finished third. He said: "I think that shows on the pitch for me.
"When you go on a pitch, and it gets hard, and you can't live up to that pressure, when you don't have everyone trying to get on the ball and show bravery. In those difficult moments, we needed to show togetherness and pull through as a group.
"We didn't do that enough when it got hard."
The 19-year-old pinpointed the dramatic defeat to Motherwell as the moment Rangers' title challenge began to unravel. He recalled: "I remember the Falkirk game before the split.
"Nico Raskin had a really good game, Youssef Chermiti was starting to score goals, and everyone was on a high as we came from behind to win.
"Then it got to the Motherwell game. But they were a really good side last year. Footballing-wise, they were top, and in that first half they played us off the pitch, to be honest. Second half, we had some new energy, got it back to 2-2. The stadium was rocking.
"The fans were helping us through it, and I genuinely thought we were going to win the game by two or three. But we missed a few chances, and then they countered and scored the winner. That was obviously a massive blow.
"From there, the pressure starts to build."
And Moore believes the subsequent defeat to Hearts exposed the fragility that ultimately destroyed Rangers' championship ambitions.
He added: "We needed to step up and play to our best. But we lost the Hearts game, and then it just became a downward spiral.
"Even at Tynecastle, we were really good in the first half, but we crumbled in the second. It was really tough to take because I did think we had the players to go win the league."