The apology was read by host James Duthie on Sportscentre on Tuesday night and posted prominently on the network's website after Phaneuf, Cuthbert and Lupul sent a letter threatening legal action earlier in the day.
The insinuating tweet about Lupul and Cuthbert was included in an ongoing social media crawl at the bottom of the screen Monday.
"In spite of TSN's protocols to prevent unfounded and inappropriate tweets from making it to air, a false, and inappropriate tweet was allowed to run," TSN said in the statement. "There was no basis for the false allegation made in this tweet. TSN unreservedly apologizes to Joffrey Lupul, Dion Phaneuf and Elisha Cuthbert and regrets any embarrassment this unfortunate incident has caused to them."
Leafs players were reportedly angry about the tweet.
Hockey commentator Bob McKenzie, one of TSN's most high-profile personalities, also echoed the network's statement on the air.
The apology was repeated again during the network's pre-game coverage of the Maple Leafs' game at Florida.
Earlier Tuesday, lawyer Peter A. Gall, who is representing Phaneuf, Cuthbert and Lupul, sent a letter to TSN demanding that the network "issue a formal apology and pay a significant amount of damages to each of our clients for broadcasting a false and defamatory tweet during their trade deadline show."
TSN did not reference the demand for damages in its statement.
Gall also said he was "sending a similar letter to the author of the tweet, Mr. Anthony Adragna."
Gall threatened a lawsuit against both TSN and Adragna if they did not comply with the demands set out in the letters.
Adragna, who later deleted the offending tweet, did not immediately respond to a message on Twitter seeking comment. Earlier Tuesday he tweeted that his "words actually getting on air is out of my control."
TSN also tweeted an apology Monday from its public relations account, calling the tweet "inappropriate and disrespectful." The network also said that it had reached out to the Leafs and "those impacted to extend our sincerest apologies for our error." It also said the tweet was erroneously aired.
On Monday, Lupul wrote on Twitter: "TSN just a poor mans TMZ. Embarrassing."
Gall said his clients will not be discussing the matter further and referred all questions to his office.