Krystian Bielik, Jack Fitzwater and Julien Ngoy all arrived on loan – from Arsenal, Albion and Stoke respectively.
Reacting to Saddlers' deadline day business, Whitney said: "It's been really, really good – at the end of it.
"There were times yesterday that you think deals are over the line but, suddenly, you get competition from another club.
"There's lots of variables. I think we have to be flexible, adapt and be ready for the unexpected – that is for all managers.
"The lads who we've got in are lads we've gone for before, in previous windows.
"We've kept tabs on them – they have been on our list to monitor.
"We went in early with a few of them, hoping that we'd build relationships.
"Julien was done at 10.59pm so I think there was a nervous twitch, but it was really good.
"I'd like to thank everyone involved."
Bielik and Fitzwater are centre-halves while Ngoy is a forward.
"They're going to bring some added strength, and quality to the group – which has already got a lot of quality in it," said Whitney.
"Defensively, we've got Krystian – who I think is going to be a top, top player.
"I think he will be an Arsenal player. I didn't think we'd get him, I thought he'd go higher, but our conversations were really good with Arsenal.
"They like the way we play, or we try to play.
"They paid a lot of money for him so he'll be really good for us.
"Jack's attitude is fantastic and it's great to strengthen our relationship with West Brom.
"Julien has undoubted ability and this is a chance to come in and cement a place.
"It'll be different for him, but that's what loans are for.
"I'm happy with the additions and hopefully they can help us kick on."