Shaw claimed they were in the game until Mohamed Salah's second for the hosts in injury-time.
He said, "Very disappointed. We didn't really deserve that - especially 2-0.
"When it was 1-0 it was really good. We had that chance with Anthony Martial. The lads gave it their all. We didn't have many chances, but those that came we should have taken them.
"We know their qualities, and there were periods where we had to defend well. Last 30 minutes we controlled it. We didn't take our chances and they took them.
On defending Virgil van Dijk's first goal, Shaw added: "Van Dijk is a massive guy and threat for them on set-pieces. It's disappointing for us.
"In the first half, over the past year - Liverpool have blown teams away in the first 20 minutes. We were still in the game until the 90th minute."