The company pointed out that nearly all teams brought forward their planned pit stop when the safety car was deployed for a second time, meaning they did around 40 laps - more than three quarters of the 52 lap race - on a single set of tyres.
Silverstone is also one of the fastest and most demanding tracks.
Pirelli said the final laps had been particularly tough "as a consequence of the biggest forces ever seen on tyres generated by the fastest Formula One cars in history".
It added that the front left tyre, which takes more punishment than the others at Silverstone, had been under "maximum stress".
Silverstone hosts another race this weekend, the 70th Anniversary Grand Prix. Pirelli said softer compounds would be used, which should rule out such long stints and turn it into a likely two-stop race.
"Also the usage prescription will be reviewed, increasing the minimum tyre pressures to reduce the stress on the construction," it added.