A solitary Luis Alberto goal saw the Romanians beat Manchester United 1-0 at Old Trafford on December 5, but Cluj ultimately dropped into the Europa League despite collecting 10 points in the Champions League.
Inter, meanwhile, have juggled two qualifying rounds and the Europa League group stages with a hectic Serie A schedule and, despite having won the Champions League as recently as three years ago, Stramaccioni is loath to describe Cluj as underdogs.
He told inter.it: "Cluj cannot be underestimated. They've done good things in the Champions League and they are a team to be respected. I also hold their coach in high esteem.
"We will be focused when we take to the pitch. We cannot think about the final at this time, we're taking each game as it comes."
Inter defender Cristian Chivu had hoped to line up against Romanian opponents for the first time since he left Universitatea Craiova for Ajax in 1999 but Stramaccioni is reluctant to use him on Thursday.
"Chivu has a slight muscle problem," Stramaccioni added. "He's an important player and I need him to recover properly."
Cluj boss Paulo Sergio and his players spent some of the Romanian winter break at a training camp in Marbella before flying to Milan early to adjust to a cold climate.
Sergio, the former Hearts manager, told the Edinburgh Evening News: "It is going to be different from what they were used to in Marbella.
"It is important that we adapt and don't find excuses. We will do everything that we can to make sure that we get a positive result. This is what football is about."
Sergio is warning against any hubris at the San Siro despite the heroics of December.
"Yes, we have beaten Manchester United but I think that this is probably going to be even more difficult," he added.
"That night was a good experience for everyone involved but now we have to put it behind us and get on with the game that is ahead of us.
"We have to think that we can do something in Milan, although we know that it will be very difficult. They have everything that a manager or supporter would like to have available to them."