Saturday's 2-0 loss at The Hawthorns saw Sunderland slump back to the bottom of the Premier League table and the players were booed off at both half-time and full-time by those fans who travelled.
The Black Cats, suffering with absences through injury and players away at the African Nations Cup, have now lost nine of their 11 away matches in the league, scoring just six goals, and are three points adrift of safety.
Moyes said: " I totally understand them
I'm a supporter myself, maybe if we had three points more we might be where people would expect us to be
But we are not that far away
A win would have taken us out of the relegation zone
"The performances recently have not been how we would have liked - and we are the first to admit that - but there are mitigating circumstances for that
"Sunderland fans have been in this position before - they have seen the team further away (from safety) before
If any fans know about this situation it is our supporters in recent years."
The "mitigating circumstances" Moyes referred to include a crippling injury list which sees Jordan Pickford, Jan Kirchhoff, Steven Pienaar, Duncan Watmore, Paddy McNair, Lynden Gooch and Lee Cattermole all unavailable while Lamine Kone, Wahbi Khazri and Didier Ndong are at the African Nations Cup
Sunderland do not play again until Tottenham visit the Stadium of Light on January 31 and Moyes hopes that will allow him to boost his ranks with players returning to the squad
"Having Victor [Anichebe] back was a big positive for us, however, he did pick up a knock so we will need to check on that
We've got over a week until our next game now, hopefully that will let us get some more players back in training, we need it."
Superb first-half goals from Darren Fletcher and Chris Brunt gave West Brom a fifth win in six home matches, keeping them in the frame as contenders for European football next season
As well as getting on the score sheet, Fletcher was the driving forced behind the success, winning plenty of second balls, barely surrendered possession and kept the Baggies ticking along
And the captain's performance drew praise from manager Tony Pulis, who said: " Fletcher is fantastic
He's been wonderful in the dressing room, on and off the pitch, he's got great respect in there and everybody's pleased
"He's one of those players
Every time he does something well, you're pleased for him."
Pulis was able to give a debut to latest news signing Jake Livermore, following his arrival this week from Hull, and the West Brom boss added: " It was difficult for Jake
Kempy (Dave Kemp, assistant manager) didn't want to get him on there because he's not worked with us, he just turned up Friday
"He doesn't know what we do, what we don't do, how we do it, and we're very structured in a lot of ways
"I'm pleased (with the signing), he'll bring a lot to the table but he'll have to learn what we want to do and the way we want to do it."
Source : PA
Source: PA