Ramsey will join Juventus on a free transfer on July 1, after accepting a deal in February that will see him earn as much as £400,000 per week.
Sanllehi says it would have been irresponsible for the Gunners to match the “incredible” offers the Wales midfielder received from other clubs, when he entered the final year of his contract.
“One of the key things for me – and I’ve seen that happening in other clubs – one of the key things is to keep the rationality in the salary balance of the team.
“Because of our circumstances, because of not renewing Aaron on time, we were in a situation in which Aaron had incredible offers building up on the salary.
“He was really keen on staying with us, he was ready to make the effort but at the end of the whole process we had to be responsible for ourselves and protect the interests of Arsenal. We realised we were going to cause an imbalance that would have been very harmful for the team’s sake in the medium and longer term,” he told Arsenal’s website.