The Giallorossi, who visit Parma on Sunday evening, lost 2-1 to Cagliari on the opening day of the campaign before holding Inter Milan to a goalless draw.
Roma let two more points slip away in Thursday's 1-1 result against Siena when defender Roberto Vitiello struck a late equaliser to deny Roma their first win of the Serie A season.
"I am worried because I'm not happy with the situation," Luis Enrique said.
"When things don't go well, I take full responsibility.
"We are missing a victory that would free the players."
Luis Enrique, who replaced Vincenzo Montella at the helm of Roma this summer, admits he did not expect such a challenging start to the campaign.
"We didn't start the campaign the way we had hoped to," he said.
"It's a difficult situation. We are lacking confidence to go in search of victory.
"We simply need to come out of this situation."
A lack of goals has been Roma's main problem so far.
The Eternal City giants have found the net just twice in their first three games and Luis Enrique will be desperate for Bojan and captain Francesco Totti to open their accounts for the season on Sunday.
Parma host Roma on the back of a 3-0 defeat at Fiorentina in midweek.
The result was their second loss on the road this season.
Parma failed to test Fiorentina goalkeeper Artur Boruc in midweek and coach Franco Colomba has demanded a vast improvement on Sunday.
"We are struggling to find the finishing touch," Colomba said. "Two goals in three games is not good enough.
"We have to continue to work and improve.
"I'm certain that sooner or later the goals will come."