The Saints came from behind to level the scores in the grand final last weekend and force a replay, but they were no match for the Pies the second time around.
Collingwood led by 27 points at the main change and kicked away in the second half to secure the club's first premiership in 20 years.
The Saints have played in three grand finals in 12 months without tasting success, but Montagna denied the heartbreak of this defeat would push his side over the edge.
"We'll stick together. We won't fracture. We're a tight club. We'll stick fat; suck it up and go again," Montagna said after the game.
"We felt resolve as a playing group this year. There was a lot externally going on, but internally we never fractured or wavered in our determination to win a premiership.
"There's a lot said about the Saints' 'bubble' and we stay in it. We look after each other and focus on what we can. If anything [the events of this season] have made us mentally stronger. We just didn't get what we wanted today."
St Kilda was without Jason Gram (concussion/shoulder), Sam Fisher (hamstring) and Robert Eddy (broken arm) for big chunks of the game, but Montagna said there were no excuses for his side's second-half capitulation.
"We still had belief at half time because we did it [came from behind] last week. In the second quarter we had our chances and got on top of them, but we didn't take our opportunities," Montagna said.
"All credit to Collingwood. They outran us and outplayed us. They were too good. There's no doubt some blokes would've struggled to get up from last week, but it would have been the same for Collingwood."
Fisher, who went into the qualifying final against Geelong with a query over his hamstring, came from the ground clutching the back of his leg midway through the third term.
The rebounding defender didn't return after three-quarter time, but said he'd asked the coaches to put him back on.
"My hammy was [torn] good enough not to go back on. I wanted to go back on, but that was up to the coaching staff and they told me not to," Fisher said.
"If I was going to do it [injure my hamstring] I wanted to rip it right to pieces, but that was their decision not to put me back on."
Collingwood's runaway grand final win on Saturday has prompted suggestions the club is about to embark on a dynasty and Fisher said it was up to St Kilda to reach the Pies' standard.
"We put in a lot of hard work and haven't got what we came here to get, but we've got to suck it up. We've got to improve again and go again next year," he said.
"We'll try and have a better pre-season if we can and we've got a gap to bridge, so that'll be the focus. In terms of hurt it's exactly the same."
Join the grand final conversation on Twitter: use #AFLGF in your tweets.
