West Brom youngster Wright signed for Town on loan for the remainder of the campaign, but was recalled a day later due EFL regulations.
Glovers boss Way has already added three other faces to his squad and hopes to complete another one in the near future.
“We’re disappointed and wish Andre all the best,” he told YTFC’s official YouTube channel.
“These things happen; you can’t blame anyone. We’re in a high-pressure environment and mistakes are made.
“We move on to the next signing and hopefully we can get on in soon.
“We’ve been speaking to one or two clubs and there’s a big, big process that goes behind signing a player.
“There’s so many things that need to fall into place and I’ll make sure we do our homework on the next one.
“We’re looking at both markets. It’s about making sure the player is right for the football club and they’re happy to come here.”