Inter, who host fourth-placed Lazio on Sunday, have won just two out of six matches in all competitions since Mancini returned to San Siro last month and sit 11th in Serie A.
However, the former Manchester City boss has not given up hope of achieving a lofty position.
"The lads are looking good, we just have to make sure we keep improving. It's always better after a win," explained the Italian, a former player and coach with Lazio.
"We've lost two games so I can't be happy. I'm pleased with the atmosphere around the team. There's still a long way to go in the league. I think we'll be in the mix for third place.
"We mustn't look at the table for now, just keep on putting points on the board. All the sides above us are battling for third place. We need to put together a run of good results.
"A win [on Sunday] would be a boost for our self-esteem."
Midfielder Hernanes, another Lazio old boy, may return this weekend after recovering from a leg injury.
"Hernanes is better now and trained with the team all week. He'll start on the bench and could play," said Mancini.