Iachini’s men produced a solid performance to beat Hellas Verona 2-1 last weekend.
The result was the Sicilian outfit’s seventh triumph since gaining promotion to Serie A last year and lifted Palermo to seventh place.
Palermo have lost just one of their last 13 league games and are 12 points clear of the drop zone.
“We are doing well,” Iachini told the Italian press. “But we cannot get carrried away. Our main aim remains to defend our Serie A status.
“Once we achieve this, we can concentrate on other targets.”
Palermo have not won on the road since beating AC Milan 2-0 at the San Siro on November 22 and have taken four points since away from home.
Rivals Inter are desperate to end a three-match losing streak in all competitions.
Inter coach Roberto Mancini is looking for an immediate response from his players after his team conceded another last-gasp goal to crash out of the Coppa Italia 1-0 at Napoli on Wednesday.
Inter also leaked late goals in their previous two Serie A games, against Torino and Sassuolo, which ended in defeats, and Mancini was upset that Napoli had also notched late on to steal the victory.
“You just can’t concede a goal like that,” Mancini told Inter’s official website.
“The goal we let in was absurd. We shouldn’t have lost this game. We did the same on Sunday against Sassuolo.”
Mancini has steered Inter to just two league victories since replacing the sacked Walter Mazzarri in November.
Inter have won just one of their last six games and lie 13th in the standings.
The Nerazzurri will be without Ghanaian defender Isaac Donkor, who must serve a one-match ban. The visitors will be without suspended defender Sinisa Andelkovic.
Inter will have to keep a close eye on Palermo attacking pair Paulo Dybala and Franco Vazquez.
The Argentinian duo have combined to score 17 of their team’s 34 goals so far.