Lennon's former number two was promoted to the top job just 24 hours after he was axed on Monday.
But Craig insists there has been no fall-out between the pair.
He said: "I spoke to Danny last night. He wished me all the best and said he hoped I could take the club on again from the great foundation he had laid.
"Will this have any impact on our relationship? No, football is football. We've build up a very good relationship over the last three years.
"I would hope it would remain as close as it has been. Danny is a terrific guy, a superb manager in terms of his work ethic, his knowledge of the game and his hunger.
"He will be back soon, very soon."
Lennon was told by Saints chairman Stewart Gilmour his contract - due to expire next month - would not be renewed despite keeping the club in Scottish Premiership.
The former Cowdenbeath manager had twice lead St Mirren to eighth place - the club's highest finish since 1989 - and landed the 2013 League Cup during his four-year reign.
But a clutch of poor signings and failure to break into the top six counted against him.
Now Craig - who will be assisted by player/coaches Jim Goodwin and Gary Teale - admits he is under pressure to do even better than his predecessor.
"It's a big challenge because the foundations Danny has laid down are there to be built on," said the 63-year-old, whose only experience as a boss was a six-month stint in charge of Belgian outfit Charleroi four years ago.
"There will be an expectation there next year because we finished eighth - can we go higher?"
With just nine registered players left and another 11 out of contract - including the highly-rated Kenny McLean - Craig now faces a race against time to finalise his squad before next season.
"We start work on that now," said the former Hibernian, Celtic and Aberdeen assistant manager. "It's going to be a massive job. Bigger than last year. It will be a huge task ahead to try and get the right players in.
"I will be speaking to the players over the next 48 hours but so far I haven't spoken to any yet."
The news that club captain Goodwin and former Scotland winger Teale were being promoted to back-room posts came as a surprise to both.
As late as Saturday the out-of-contract duo were still unsure if they were being kept on by the club.
But Goodwin, 32, said: "It's been a hectic 24 hours. I was out in my back garden yesterday cutting the grass when I got a call to come into the club.
"I wasn't told what it was about and hoped it might be to talk about a new deal. But when I came in Tommy was there with a couple of directors and I was flattered to be asked to join the coaching set-up. An offer I can't turn down.
"However, I still believe I have a big part to play on the park. It won't be too difficult to juggle the jobs. I'll probably need to be in a bit earlier and get home a bit later but hopefully I can act as a voice for the players to Tommy."
The new assistants were among a clutch of senior pros who did not join up with the younger members of the Saints squad who jetted out for and end-of-season jaunt to Ibiza.
And Teale admits both he and Goodwin will now take a small step back from the rest of the playing staff as they prepare for their new roles.
"I've had a few texts saying congratulations from the boys," he said. "They are out there enjoying a deserved break in Spain after a hard season and I'm sure they will be toasting the new appointments.
"But the older you get you do begin to take a wee step back and that will continue now.
"I've got a great relationship with the players but then I'm not 21 any more, I'm not doing the the things you do at that age when you are out enjoying yourself. But hopefully that relationship will continue."