With fellow left-back Milos Kerkez arriving from Bournemouth, Robertson concedes he was forced to weigh up his options at Anfield.
"It was the first summer I really had to think about my future," he said in a press conference for the Scotland national team.
"I've always had clear ideas, but after a difficult season and with competition from new arrival Milos Kerkez, I had to weigh everything."
Robertson admits he had an offer from Atletico Madrid and asked for time to decide, analysing with his family the impact of a move to Spain, especially from a personal perspective, with two young children.
Ultimately, he chose to stay at Anfield.
"I don't regret it," he added. "I made a decision, and I'm convinced that if I continue to work like this, I'll play a lot of games for both Liverpool and Scotland."