The on-loan Celtic teenager knows he owes a debt of thanks to the outgoing manager for showing faith in him.
Roberts, who was named Scottish Player of the Month for April, scored two fine first-half strikes as the Bhoys sealed a fifth Scottish Premiership title in a row with a 3-2 win over Aberdeen on Sunday.
The 19-year-old has been a big breakthrough star at Parkhead since joining the club on an 18-month loan deal at the end of the January transfer window, scoring five goals in 11 appearances and showing the kind of flair and skill which convinced Manchester City to pay around £12 million for him last summer.
The England Under-19s international revealed that Deila came to see him play for City in an attempt to convince him to join the Hoops, and Roberts will always be grateful for the part the Norwegian has played in his early career.
Roberts told the Celtic website: "He came to see me when I was at City. He wanted me in his side and he expressed that to me and it’s always good when a manager really wants you and wants to play you.
"Coming here, he was patient with me. He explained to me what he wanted me to do and he had faith in me to put me in the team so I’ve got pure respect for me and I thank him a lot."
With the title now secured, Roberts knows he will have a new manager to impress when he links up with his teammates for pre-season ahead of the new campaign, but if he can replicate and build upon the performances he has put in in recent weeks, he will surely have a big role to play for the Bhoys.