They point to figures showing a nearly five-fold increase over two years in the number of children and young people waiting more than 14 weeks to be seen.
Leader Kirsty Williams said mental health was seen as an "afterthought".
The Welsh government said it would spend an extra £7.6m a year to ensure young people were assessed quicker.
The Liberal Democrats found that in April 2015 there were 1,332 children who had been waiting over 14 weeks to be assessed by psychiatric services, up from 282 in April 2013.
"These figures are appalling and show that mental health waiting lists are spiralling out of control," said Ms Williams.
"For too long mental health services have been an afterthought of governments. This complacency means our mental health services are miles behind where they should be."
A Welsh government spokesman said an extra £7.6m a year would be spent to ensure young people receive "the right treatment at the right time".
He added that work was needed to cut the number of "unnecessary referrals", with a 100% increase in children and young people seen by child and adolescent mental health services (CAMHS) over four years.
"Services tell us that around a third do not have a problem requiring any intervention and are discharged at once, and a further third of referrals do not need specialist treatment," he said.
Mental health waiting lists are "spiralling out of control", the Welsh Liberal Democrats have claimed, accusing ministers of "complacency".