Wellingham named the Eagles on Thursday evening as his preferred destination after wanting to pursue a career extension in his native state of Western Australia.
He used West Coast's website to say he felt it was "time to move on", and he would head overseas in the coming days and leave the two clubs to facilitate a trade.
Beams, who won Friday night's Copeland Trophy, said while Wellingham's close friends at the club might have been aware he was leaning towards heading home, he didn't know.
But the Queenslander said he understood Wellingham's plight of living away from his home state.
"I think Sharrod's made it public that he's going and that's sad, he's a great bloke and he's someone you want around your footy club," Beams said.
"At the end of the day, footy's a business and his family is back in WA and you certainly can't hold it against him for wanting to go home and be with his family.
"There's been times in my career where I've thought about going home and being with my family but I love this place and I love the footy club and the blokes I play with so it's never been an option for me.
"I'm sure his closer mates would have known but I didn't.
"It's become news to me over the last couple of days. I never thought he'd leave but obviously he's missing his family."
Beams said he wasn't sure what was happening with Chris Dawes, who has asked his manager to seek other opportunities after the recruitment of free agent and West Coast forward Quinten Lynch this week.
The former Eagle is expected to arrive at the club in the middle of next week.
Gillette Trade Period hub
Both Wellingham and Dawes were in attendance at Friday night's best and fairest count, which indicated there was no bad blood existing between the players and club despite their likely departures.
Club president Eddie McGuire paid tribute to Dawes, who injured his knee in the semi final against West Coast and played in the preliminary final loss to the Sydney Swans with heavy strapping and limited mobility.
"There were some heroic efforts this year," McGuire said.
"A favourite of mine, and we're not sure which way it will go, but I also thought the last game and finals effort from Chris Dawes was fantastic with the way he fought hard for our club with his knee injury.
"The changing face of football makes things very difficult at times but things like that are never forgotten at this football club and you know the feeling you're held in by everyone here, including your teammates."
Trade Machine
Coach Nathan Buckley said the preparation for season 2013 had already begun, exactly two weeks after the Pies exited the premiership race at the preliminary final mark.
He also said there would be no holding back in ensuring the club got back to where it wanted to be, after potentially basking too much in the success of 2010 this season.
"There will be personnel changes; there's no doubt about that," Buckley said.
"As time goes by, and there's are always changes as the AFL mandates it. You've got to have three or four changes every year.
"The club will make no apologies for demanding and expecting high performance, and then to be looking for that year by year and then day by day when we get into our season."
Meanwhile, it is believed Tyson Goldsack will remain at Collingwood and is close to finalising the finer details of a new contract.
He joins Ben Johnson, Andrew Krakouer and Brent Macaffer as players likely to continue as Magpies in 2013.
The Pies' 2013 campaign starts on November 21 when the first-to-seven-year players return, followed by the rest of the list on November 28.
They then head to Utah for a pre-season altitude camp on December 4.
Jennifer Witham is a reporter for AFL Media. Follow her on Twitter @AFL_JenWitham.
