Speaking at the announcement of funding in Belfast on Thursday morning, before Higgins gave his reaction, Lyons said the location of clubs had not come under consideration.
“This hasn’t been done in terms of geography, it has been done in terms of need and other criteria that we set out,” Lyons said.
“Yes, you can look at the two big ones in Belfast but there are many others throughout Northern Ireland.”
Institute chairman Bill Anderson said he was at the “depths of despair”. Institute had put in for £14m to develop a new stadium and community hub at Cloney Park West, and Anderson said he was “devastated” for those connected with the club.
“It’s hard to get your head around. I’m very disappointed and it will take a while to process,” Anderson told BBC Radio Foyle, adding that the club will likely remain playing at the Brandywell for the foreseeable future.
“We will reflect on it. When we set out this vision we had the Waterside community in mind and we didn’t believe we could deliver what Waterside is entitled to on less than £6m.
“That would have given us a pitch, a stand and some changing rooms, but now the vision we had for the greater Waterside community.
“I thought our footballing need and community need was really high, so I don’t really understand the process.”
From a Coleraine perspective, Higgins said not progressing to the next stage was a “setback” for the Bannsiders, who “could do with a bit of help as well”.
“For me, there’s a bit of anger and a bit of frustration,” he added.
“In my opinion, and a lot of people would back me up, it’s a part of the country that gets neglected.”
Derry City released a statement saying the club “noted” the decision and “will take time to reflect and discuss our options going forward”.
