After starting the season well, Inter tailed off and have looked to be in danger of missing out on the top four for a while.
And Spalletti accepts Inter cannot afford to keep dropping points if they want to secure a return to Europe's elite competition, which they have not featured in since 2011-12.
"There are increasingly fewer and fewer opportunities, which means they are worth more than ever and must be exploited," said Spalletti ahead of Saturday's trip to Atalanta.
"We have to pick up a good result [against Atalanta] and give ourselves a chance to get back into the first four before the Rome derby.
"Everything is still in our hands, it all still depends on us. Myself, the team and the whole environment at Inter. We all know fully well who we are and what our situation is.
"We're where we expected to be and this is what we were aiming for at the start of the season. We're prepared for this final rush."
Midfielder Rafinha, who is on loan from Barcelona, was recently quoted saying he wants to remain at the Italian club permanently, and Spalletti is clearly an admirer of his.
"Rafinha is a good footballer who can give us a big hand," he said. "Inter knows and knew in the past how to get by even without such players.
"He has to be evaluated from time to time, but he's certainly a strong player and he's currently in the right shape to be picked for a strong team such as Inter."