Forest led for most of the match after Henri Lansbury scored in the first half, but Pugh scored in the 91st minute to secure a valuable point away from home and Howe believes it was the very least they deserved.
"I felt we deserved it. The lads put in a really good second half performance and dominated the game," he told BBC Radio Solent.
"Whenever you're chasing a goal, you can leave yourself vulnerable at back but we defended well.
"We did a lot of things right and if we had been beaten it would have been hugely disappointing, so it was a big goal for us."
The point leaves Bournemouth in ninth position in the Championship, five points off the play-off places.