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.
“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.”
One player who came to the club this month is Jake Beesley, who arrived at Bloomfield Road from Rochdale.
The striker is in line to make his Blackpool debut today as the Seasiders return to league action with a home clash against Millwall after last week’s fixture against Barnsley was postponed.
Assessing Beesley’s time with the club so far, Critchley said: “It’s going to take time to adapt, so the more sessions he has the better it will be for him.
“I don’t like overloading players with information when they first come into the club because they have so much to think about, like a new way of training, different sessions, different way of playing, new teammates, sometimes players have to move, so they have a lot going on.
“I just want him to be himself first and foremost, relax, enjoy the environment, enjoy the training and we can just start to drip feed certain bits of information we feel could be helpful in the future.
“Jake has made a positive impression on everyone so far.”
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