Rudi Garcia's men were held at the Stadio Olimpico by a troubled Parma side - who sit six points adrift at the foot of the league while also contending with financial difficulties - leading to jeers from some supporters.
With leaders Juventus only able to draw with Cesena later on Sunday - Roma remain seven points off top spot but, following his debut, Doumbia feels he will continue to improve following his Africa Cup of Nations exertions with the Ivory Coast.
"My first few days here have gone really well," the striker told reporters on Monday.
"We needed to beat Parma to make up points on the leaders. All I can say is that I'll do everything in my power to turn those boos into applause.
"It's true that I'd only trained twice before the game but I played in the Africa Cup of Nations final.
"I'm a centre-forward, I like to be in the box. I've scored lots of goals in the past. I need confidence to be able to perform at my best and I'm sure I'll get that here.
"I haven't played much recently but I'm going to work as hard as I possibly can to reach peak form and finish this season on a high."
Doumbia also spoke of the impact club and country team-mate Gervinho had on his move, adding: "I was at the Africa Cup of Nations when I heard of Roma's interest in me.
"Gervinho has been talking to me about Roma for the last two years on international get-togethers. That was another reason for me to want to come here.
"I don't think Roma are that different to the side I played against in September when I was at CSKA [in the UEFA Champions League].
"All teams go through tough spells over the course of a season but even if we didn't play well against Parma, we're still second in the league."
