The Spaniard was axed earlier this season and replaced by Graham Potter. Lopetegui only took charge of the Hammers last summer after replacing David Moyes.
Asked about turning down the Belgium job, Lopetegui told AS: "We had important things, but it wasn't the right time. I'm one of those who have to digest what happened. We decided to wait.
"At the time we had a feeling of disappointment - going back to the farewell to West Ham. The team was where it should be. The team was thirteenth and with options to finish ninth or tenth, which I think is where we should be.
"It was the idea of the first year, to get to know each other better. We lost against Liverpool and City, we were far from the relegation zone. I was surprised by the sacking because we had the trust of the players. We were in a moment of change, we accept it.
"West Ham is a club with several shareholders and we had a very good relationship with all of them. Nobody told us we were in danger.
"(Tim) Steidten? I won't talk about him. I have always had a good relationship with all the sporting directors I have been involved with, even with different views."