Alonso, 33, was the quickest of the drivers not powered by a Mercedes engine, but could only manage seventh place on the grid for tomorrow's race at Monza.
The Ferrari driver claims that he could not have achieved a better result even if he had "100 sets of tyres".
"I was completely on the limit today," Alonso told reporters. "I had two runs in Q2 and two runs in Q3 and I did four identical laptimes, so I could put 100 sets of tyres on and I would do identical laptimes. It was absolutely the maximum.
"Obviously Mercedes and Williams are a little bit too fast, and then there is a group of Ferrari, McLaren and Red Bull quite close in one or two tenths, so hopefully we can lead that group.
"Tyre degradation will be important in the race. Probably we have to make a lot of laps with the soft and a lot of laps with the hard tyre so we just need to have everything under control if possible."