The World Cup qualifying triumph in Cardiff on Friday night was the national team's first win since Coleman replaced the late Gary Speed at the helm in January. The Dragons had endured a disappointing start to the campaign, opening with defeat to Group A favourites Belgium before suffering a 6-1 thrashing in Serbia.
But Morison believes Wales can now look forward to their next qualifier in Croatia on Tuesday with optimism, and said: "We always had the belief. We kept it from the games when we had been winning, even though we had lost a few."
He went on: "We have a great spirit and a great camp and we enjoy getting together. Everyone is turning up, which is fantastic, and we will carry it on until Tuesday night and hopefully we can put on a good performance in Croatia.
"We have always been behind Chris and I think we showed that we are a very good team. I thought we made Scotland look very average."
Scotland took a first-half lead through James Morrison, before a Steven Fletcher goal was harshly disallowed. Gareth Bale then sparked the comeback when he converted from the penalty spot with 10 minutes to go, before securing the win with a stunning strike in the final minute.
Morison said: "Thank god for Gareth Bale, eh? It was fantastic. As soon as he got the ball, we were all screaming 'shoot' because it seems he can do no wrong at the minute. It was a fantastic goal.
"I always thought we had a chance. We were the better team from start to finish.
"We should have won a lot more comfortably. As long as we win the games, it doesn't matter."