Celtic manager Neil Lennon admitted he was beginning to consider his future when his side were 3-0 down at Rugby Park in October, days after losing at Hearts.
But a dramatic late fightback began what would then have been an inconceivable 27-match unbeaten run in domestic football following an inconsistent start to the campaign.
A recent 20-match winning run in Scottish football has furnished Celtic with huge confidence and Matthews is determined to make that count in the Scottish Communities League Cup final against Kilmarnock on Sunday.
Matthews said: "We came back from three down and we haven't looked back from there. That was a big turning point in our season.
"We know it's going to be a tough game, they have showed that whenever we have played them this season.
"But I think we are a different team than we were back then and we are fully confident we can go and win the game.
"Anything can happen on the day in a cup final. Nerves can get the better of you but we are fully confident we can win the game."
The 20-year-old believes attitude is the key difference in the Celtic team from before the Rugby Park encounter to now.
"It's hard to explain," said the former Cardiff player, who started Sunday's 4-0 William Hill Scottish Cup win at Tannadice.
"We just go into every game thinking we are going to win and I think that shows in our performances.
"Even against Dundee (United) we didn't start that well but we felt if we kept going we would eventually grind them down and win the game, which we did. I think that's the big difference really.
"At the start of the season we had a lot of new players and it took us time to gel but you can see in our performances over the last few months, we are starting to understand each other a lot more.
"That's bringing out the best in us."
Kilmarnock have only won one game since their semi-final over Ayr but that came against Rangers, their second victory over the Ibrox side this season.
And Killie goalkeeper Cammy Bell believes they can upset the odds.
"I think our chances are good," he said. "Both teams start at 0-0.
"They need to score against us first and it's obviously up to me to keep the ball out the net.
"Hopefully I can take my recent form into the game on Sunday and stop them from scoring and you never know what can happen, it's a cup final at the end of the day."