The young striker picked up the booking in stoppage time of the first half for shooting after being flagged offside and it will see him ruled out of the next FIFA World Cup qualifier against the Ukraine on Tuesday.
Hodgson, who watched the Manchester United star hit two past the visitors, now faces further selection worries, with his attacking options already depleted courtesy of injuries to Wayne Rooney and Daniel Sturridge.
"We were already very short of front players," he said.
"I don't believe it was a yellow card offence, and the other one he got in Montenegro, we should have had a penalty and he was booked for diving.
"He's been unbelievably unfortunate. We have already lost Wayne Rooney and Daniel Sturridge and it makes life difficult for us. It takes the gloss off a good team performance."
Hodgson remonstrated with the officials following the punishment, but he can at least take comfort from his decision to include forward Rickie Lambert in the ranks.
The 31-year-old, who plays for Southampton, made his first international start following a cameo appearance against Scotland in August and he grabbed his second goal in as many appearances.
He headed home in the 26th minute to add to Steven Gerrard's effort 14 minutes earlier, and then also set up both of Welbeck's goals.
