The Real Madrid forward will be suspended for Wales' next World Cup qualifying match after being booked in the 0-0 draw away to Ireland last Friday.
Bale was given the yellow card for a foul on Ireland defender John O'Shea in the second half and the suspension leaves him unable to help his side in June when they travel to Belgrade.
Wales will be looking to halt a run of four consecutive draws that has left them sitting third in Group D, four points behind Serbia and Ireland in the race to reach Russia next year.
"You take someone like Gareth Bale out of your team and you are going to miss that," Coleman said to the Daily Mail.
"We have got to find another way and we will.
"That will be our sixth game in this campaign and we have had Aaron Ramsey for [only] two of them. Joe Allen has missed a couple too.
"But at our best we know we can play against anybody and win."
Ireland manager Martin O'Neill and O'Shea have both criticised Bale's tackle, but the 27-year-old LaLiga star felt he was unfortunate to have received a booking for the incident.
The fiery match also saw Neil Taylor sent off for a challenge on Seamus Coleman that left the Ireland captain with a broken leg.