Roberts, 19, has been used mainly as a substitute since joining the Scottish champions at the end of the winter transfer window.
“The manager knows what I can do and I always do my best whenever I am on the pitch,” said Roberts.
“I trust his judgement. He picks the team and I have to do whatever I have to do.”
‘Fans are who you play for’
Hearts briefly led at Celtic Park through Jamie Walker’s impressive strike, Gary Mackay-Steven levelling.
And Roberts, signed by City from Fulham for around £12m, came to the fore by finishing well either side of half-time to secure the three points for Deila’s men – moving them seven points clear at the top of the Scottish Premiership.
“It is a challenge for everyone,” added Roberts. “Everyone wants to play in the team and be involved.
“You wouldn’t be here if you didn’t want to do that, so yes, everyone is competing, but it is healthy and good for the club and we are pushing in the right direction.
“I just enjoy playing football whenever I am out on the field.
“It was a very good three points. My first and second goals – it was a good feeling, especially in front of all those fans.
“Fans are who you play for. Without them, you would be nothing.
“It is joy to play in front of them and score goals for them and I will try to carry on doing that.”