Evans took over from Uwe Rosler back in October, and at that time the Italian owner was apparently scared of seeing his side relegated.
Leeds have since moved away from danger, and Cellino now wants to see the Yorkshire club start mounting a play-off push.
“When I first took over the owner was worried about relegation,” Evans said.
“Now he’s told me to build a team that can compete. I’ll do that but it’ll take time. I’m confident that when players see what we do in the summer, they’ll take a different look at things.”
When Evans took charge, Leeds had won just two of their first 11 Championship matches and they were sitting just above the bottom three.
The Whites have improved under the former Rotherham United boss’s stewardship, and they now sit in 15th place in the standings.
Leeds are 11 points clear of the drop zone, making relegation a distant memory now, but the play offs also seem a long way off this season.
Leeds are 12 points behind sixth placed Ipswich Town, meaning that it looks like Evans will have the opportunity to build for next term throughout the rest of the campaign.