Pochettino – who guided Spurs to four successive top-four finishes in the Premier League, as well as last season's Champions League final – was sacked in November following a poor start to the campaign.
Jose Mourinho was swiftly appointed his successor, with Spurs winning five of their seven matches since in all competitions.
Levy made the call to dismiss Pochettino, but hinted it does not necessarily mean the end of the Argentine's association with Spurs, who established themselves as one of the Premier League's elite clubs under his guidance.
"You have to understand I had built up a personal relationship with Mauricio over five and a half years," Levy told the Evening Standard.
"It is not something I ever wanted. Personally, it was incredibly difficult, I told him that and he understood.
"He's been in football [a long time], he understands. It's not personal and I'm sure he'll come back stronger and get an opportunity to manage another great club. Maybe one day he'll come back to us.
"I'm not going to sit here and analyse the past. It's not productive. Mauricio did a fantastic job for us, we are very grateful. I wish him all the best for the future.
"I'm still in contact with him. My relationship is very good with him. It just got to the point where it felt we needed a divorce."
Spurs wasted little time in bringing in Mourinho and, though Levy confirmed other options were considered, the Portuguese was always the club's top priority.
"Many years ago, I can't remember exactly, we were linked with him," said Levy. "But I'd never spoken to Jose. We never had a conversation. And his availability was totally unrelated to Mauricio, not connected at all.
"I can't remember when I first spoke to Jose, but once I made the decision in my mind we had to make the change, although internally we knew of more than one candidate who would have been interested, Jose was absolutely number one.
"We had a number of discussions. Firstly, it was such a hard decision and you never know what you are really getting until you work with somebody.
"There are lots of perceptions out there in relation to Jose that I'm not sure are true. I wanted to spend some time with him so we were totally aligned, on the basis there was no point him coming to a club where he expected different things to us. And we were totally aligned on the strategy going forward."