The blooms from Princes Street Gardens and other parks are being sent for composting even though they would flower again year after year.
The council said it was the cheapest way of ensuring the city enjoys bright floral displays throughout the year.
But the local authority has been urged to consider giving the plants away to schools and community groups rather than mulching them.
Council workers are currently stripping out spring flowers such as tulips and polyanthus to make way for summer blooms.
Green councillor Alison Johnstone wants to see schools and other interested parties invited to a "free flower day" where they could come armed with trowels and take away the plants earmarked for composting.
She said: "There's lots of eco-schools in the city and lots of Victorian playgrounds that would welcome that burst of colour.
"While it's commendable that they are going to be composted rather than dumped altogether, if these are perennial flowers it does seem wasteful.
"I would imagine that if you had a day where people could collect the plants, they would be snapped up.
"If you gave me the opportunity to go and get a couple of baskets from Princes Street Gardens, I would snap it up."
The city council said the composting was standard practice across Edinburgh's parks as it was more economical than storing the plants for another year.
The council does keep pot plants and baskets across city buildings, unless they are seasonal and die naturally.
A council spokesman said: "Old flowers are removed and composted to help fertilise future planting.
"It wouldn't be at all economical to keep them in storage as they would need to be stripped back, cleaned and lined – a very big job which would take a lot of time.
"It's much cheaper to plant new flowers next year."
The spokesman said amateur gardeners could not be easily invited to help themselves as the plants needed to be properly removed and the beds prepared for the new plants.
Beechgrove Garden star Lesley Watson, who also runs New Hopetoun Gardens, at Broxburn, in West Lothian, said she sympathised with the council.
She said: "What we would do in our own gardens is lift them and split them and they would go on forever and ever so it does seem a shame.
"But, although it does seem very wasteful, they are trying to get the best performance from the flowers.
"It seems like a nice idea to pass them on to schools or whatever, but they will also be thinking about the logistics of it and the financial consequences.
"It's not an ideal world, but they're aiming for peak summer time when all the tourists are in Edinburgh for the Festival."