John-Jules returned to Arsenal during the week after an unsuccessful loan spell at Bloomfield Road, where he had failed to make an appearance since mid-October.
Howe, meanwhile, had his contract cancelled by mutual consent after failing to make a single league appearance for the Seasiders.
“Unfortunately the move didn’t work out for Teddy here,” Critchley said.
Tyreece John-Jules’ loan spell with Blackpool ended earlier this week
“He went to Scunthorpe at the end of last season and he’s been searching for a club. Both parties felt now was the right time to explore other options.
“He’s a really nice lad, he’s a good lad to work with, but he needs to get his career moving again now, so we wish him all the best.
“Tyreece was different. He’s a young player with undoubted talent and potential, he’s a really good boy again and a delight to work with.
“I’m sure he will have options but he needs to play on a more regular basis and that’s something I couldn’t guarantee for him here during the second half of the season.
“We were both in agreement the best thing for him would be for Tyreece to go and try somewhere else.
“Does that free up a bit of room within our squad? Tyreece leaving does, so we will see what happens.”