Wanderers secured a last-16 trip to Fulham on Sunday with a 1-0 triumph at the DW Stadium, although the victory was marred by Ricketts' injury, the Welshman going to ground in the second half while tracking Latics substitute Victor Moses and having to be carried off the pitch on a stretcher.
"That is the nature of football, but again, it is something we have to cope with, as we have done all season," said Coyle, who lost centre-back Zat Knight for up to six weeks with ankle ligament damage sustained during last weekend's Barclays Premier League win over Everton.
"At one point we were down to 15 players and we are not at that stage yet, but we do have good players - as they have shown (against Wigan) - that can step into the breach.
"David Wheater (Knight's replacement in the starting XI) was outstanding again and I thought after Marcos Alonso came on (for Ricketts) and went to left-back, with Paul Robinson going to the right, they all stuck to their task.
Coyle admitted the signs were not good for Ricketts.
"The medical team think it could be quite severe and we hope that is not the scenario," the Scot said. But the way it is looking right now, I think he is going going to be a lengthy period of time."
In a match with an attendance of just 7,515, Ivan Klasnic netted the winner for Bolton in the 66th minute, rifling the ball across Mike Pollitt and into the corner having been played in by Mark Davies.
Wigan boss Roberto Martinez, who made nine changes, did his best to remain upbeat in defeat, focusing on the performances of three unnamed players he thinks can boost the club's battle for top-flight survival. He also claimed the "soft" pitch, which is being relaid today, worked against his side.
"I felt some of the individual performances were very good and that is a positive," said Martinez. "But as a team, we couldn't adapt to the pitch, which didn't help us to put three or four passes together. We found it quite difficult and Bolton adapted a lot better.