Cahill moved to Chelsea last week for £7m and since then Premier League strugglers Bolton have enjoyed wins over Macclesfield and Liverpool.
"When you lose a player of his quality it could have an adverse effect," Coyle said. "But when things like that happen it can also bring a group together.
"I told the lads they had to understand that players come and go and when it happens they have to batten down the hatches and stay together as a group.
"The level of performance [against Liverpool] showed that."
Bolton are currently 17th in the league with 19 points from 22 games.