Dzeko's four goals in the match against Unicusano Fondi came after the striker had already notched seven strikes during pre-season - against Liverpool, Montreal Impact, AC Pinzolo and Terek Grozny.
And Spalletti believes the Bosnian hitman is very much on track as the new season approaches.
"Certain performances are always crucial in terms of making a good start and at passionate clubs like Roma - they give the momentum to go all the way," said the Giallorossi coach in a press conference. "It's also important for him given what he's been through.
"However, there's no doubting his ability. He's got technique, power, decision-making - now he just needs to add a touch of stubbornness and be constantly on the lookout.
"That said, he's got off on the right foot and wants to prove people wrong as he's shown this season - much like the way he ended the last campaign when he wanted to prove what he could do despite me not always picking him to start. He simply needs to keep working like this. He's doing well."
We're nearing 17 August, when Roma meet FC Porto in the Champions League play-off first leg but the Roma coach doesn't think it's quite time to be picking his side.
"It's too soon to ask who will start out of Alisson and Wojciech Szczesny a week before the game," he added. "When you have two top-class keepers, you tend to keep tabs on their form before making a decision. I watch and assess them and - based on what they show me - try to give them what they deserve.
"That's always my approach, that's a coach's job. I haven't said that I don't have doubts, Roma are a good team this season and when you work with decent sides there are always question marks - and then some. We have great players, in several cases two in the same position. However, I still have a few days to choose."
How far along is Kevin Strootman?
“Kevin needs to play football on a consistent basis and be involved in proper matches to get back to his best. We were wary that regular work might cause him to be a bit stop-start yet he has done everything we've asked of him. Clearly though, a clutch of proper games will allow him to rediscover his outstanding ability. He's on schedule and we're pleased and confident."
William Vainqueur featured for 90 minutes today, is that a showing of faith towards him?
"He's a player who needs to sit in front of the backline, he's strong in the challenge and is also tough when we don't have the ball. We appreciate his ability but we have to make decisions and we have other players in that position. We need to see whether he can find the right motivation. It's not easy to promise him a starting berth. There's also Leandro Paredes and Daniele De Rossi in that position. He could also make a different decision, we need to assess what he's willing to do. He has to keep doing what's he's doing and improve in terms of moving the ball quicker."
There are a number of transfer rumours surrounding Leandro Paredes. What's your take on that?
"Often people put words in my mouth that don't allow me to do my job properly with the players. Leo is a good footballer and we don't want him to leave. However in a climate like this, the better players are often those that you can use to raise funds and that goes for everyone. Napoli wanted to keep Gonzalo Higuain for instance. Then there are a lot of other things, that doesn't only apply to him but everyone else too. I think Paredes is a good player, ideal for that position and I think he'll stay at Roma."
Gerson has been with you for a month now. What have you made of him in training?
"I'm delighted. Although some people have said I'm not happy with him. He needs to adapt to the Italian game and must be willing to defend, as he's more used to playing with the ball at his feet. He's a quality attacking midfielder but needs a bit of space and struggles a touch when it gets congested. However, he's a player we're considering for selection because a big club like Roma need to be covered across the board.
"We must have enough numbers to be able to handle playing four matches in the space of a few days as will soon be the case. We need big players to come into the side, as hungry as those who are starting matches."
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