The Glasgow giants picked up the first silverware of the Scottish season after defeating Dundee United 2-0 at Hampden Park on Sunday.
Celtic will face United again on Wednesday, the third of four meetings between the sides in a fortnight, when they meet at Celtic Park in a Scottish Cup quarter-final replay.
Celtic manager Ronny Deila and his team came in for criticism at the start of the campaign when they crashed out of Champions League qualification and had some disappointing domestic results.
But Collins says the fact the club are now favourites to claim a treble for the first time since 2001 shows how far the club has come this season.
"Ronny felt the same as us all at the start of the season
We were all disappointed," Collins admitted.
"Everyone wants to hit the ground running but it never happened
We just concentrated on the next game, the next training session and we worked hard.
"Everybody has worked hard, nobody more so than Ronny - 24 hours, night and day
And we have got our rewards - our first trophy.
"We always said we want results and performances
Obviously you need results if you're Celtic manager but ultimately we want results and performances.
"It takes time
From the first month until now, we're in a much better place.
"The verdict will ultimately be given at the end of the season, but we can see as coaches as every week goes by that there is improvement."
The match at Celtic Park comes after the sides played out a 1-1 draw at Tannadice 10 days ago.
Despite their victory in Sunday's final, Deila said his side must ensure they prepare properly for Wednesday if they are to continue their quest for a treble.
"When you have something you like you should want to do it more," Deila said of the League Cup win.
"Now we have a taste of it and I can assure you that I want to win that Scottish Cup as well, so Wednesday is an important game for us.
"It's another game and it's at Celtic Park
We want to be kings at Celtic Park and it's a new game and we have to be up for it."
Meanwhile, Dundee United midfielder John Rankin says his teammates will use the disappointment of the cup final defeat to spur them on when they return to Glasgow.
"We are looking forward to Wednesday and there is a determination in the dressing-room to go and put things right," Rankin said.
"Obviously we didn't win the trophy but, as I said, there is a real determination to get through to the next round of the cup."
Source : AFP
Source: AFP