Cassell, 39, a 16-year NBA veteran who has not played this season, was dealt to the Sacramento Kings for a heavily protected 2015 second-round pick and cash considerations.
The trade, said Ainge, "creates flexibility if a player be comes available."
Asked if Allen's injury would lead him to go after another guard, Ainge said, "I don't think that changes anything we're doing or changes our mind-set.
"We like our team, depth, and talent. If a trade comes where we can improve our team, we will consider it. But we have nothing imminent."
Cassell still has interest in playing and has coaching aspirations as well. But a source close to him said he wasn't interested in playing for the Kings since they aren't a playoff-caliber team. They are expected to waive him.
The Sacramento Bee reported that the cash involved in the Cassell deal was about $500,000, and that the Kings made about $340,000 on the trade.
In addition to a scoring guard in light of Allen's absence, another need for the Celtics would be a big man. While Ainge praised reserves Glen Davis and Leon Powe, both are considered undersized at less than 6 feet 10 inches. Patrick O'Bryant, a 7-foot center, rarely plays.
Free agent big men available include Robert Horry, who is expected to stay retired, Michael Doleac, Othella Harrington, and ex-Celtic Scot Pollard. The Celtics also could sign an NBA Development League player to a 10-day contract.
"Refining our bench is what we're trying to accomplish," said Ainge. "We have big-money guys that our team is built around and are not trading. Anything we do would be to solidify the bench."
Allen was injured during practice before the Celtics started their current road trip with wins at New Orleans and Dallas last week. Rivers said that when he was a player, he sustained a similar thumb injury during the offseason.
" 'Gatekeeper's Thumb,' they called it," Rivers said. "I don't know what a gatekeeper is - back in the day, a lot of them got hurt. It took quite a while [to heal]. When someone told me four weeks, I know it takes longer than that."
