After a poor start to the 2014-15 Serie A campaign, head coach Walter Mazzarri departed the club and was replaced by Roberto Mancini, returning for a second stint in charge.
On Monday, Mancini earned his first league win since arriving back at San Siro, as goals from Mateo Kovacic and Andrea Ranocchia saw Inter to a 2-0 success over 10-man Chievo.
That victory leaves Inter 11th in the table, but with only six points separating them and third-placed Lazio - their next opponents on Sunday - in the table, D'Ambrosio believes a top-three finish is a realistic aim.
"We're aiming for third spot because we're Inter and we need to aim high," he told the club's official website.
"Winning is always important but we need to capitalise on this by getting a good result on Sunday.
"We must put together a winning run - getting the three points [against Chievo] will mean nothing if we now go and lose to Lazio.
"The team needs confidence and that's something you can only get with time. We're working hard to prepare for matches in the best way possible and we're putting Mancini's ideas into practice."
Inter have been drawn to face Celtic in the UEFA Europa League last 32 in the new year, and D'Ambrosio is expecting a difficult test against the Scottish champions.
"Every match is different. It'll certainly be a tough one, and we'll need to have 100 per cent concentration because we really want to do well in the Europa League," he said.
"There are more matches in the league, so if you slip up you have a chance to put that right next time out. That's not the case in European competition so it's more difficult from that perspective."
