Ten Hag was given his marching orders at Old Trafford last November before being replaced by Ruben Amorim as Man United endured their worst ever Premier League season.
Shaw, 30, has had several injury issues to contend with over the past few seasons and only played 34 times for Ten Hag during his two-and-a-half-year spell at the club.
Speaking to The Athletic, Shaw admits he felt like he let his former manager down due to his consistent injury problems.
He said: “I kind of felt like I let Erik down with the injuries and stuff. I wasn’t there for him towards the end, and that wasn’t nice.
“Then, when the new manager comes in and we speak about different things, different aims for the rest of the season that we had, obviously then again I get injured.
“A lot of last season, I just felt like I let a lot of people down, in the club and the team, because I was always injured. I might not have been but it was just something in my head where I found it really hard. I put a lot of blame on myself.
“The team and the manager were really good with me. Especially the manager, he stuck by me.”