Despite falling behind to a Scott Dann strike, the Cherries levelled through Marc Pugh before Benik Afobe headed a second-half winner. And Howe was quick to praise the fighting spirit of his side.
"When we went a goal down we had to show real resilience," he explained.
"We weren't very good in the first half but that goal from Marc Pugh was important, to score so quickly after.
"It gave us a life line because we were second best in the first half and dipped below our usual levels. But we responded brilliantly and, I felt, just about deserved it in the end."
Afobe's winner marks the striker's third goal in his first five games for the Cherries and Howe heaped praise upon his latest recruit.
"I was really happy to see that second one go in," he continued.
"It was what I felt we deserved and another good for Benik, which is great for him.
"He's still only young and has a long way to go, but we believe in him, both as a player and a person.
"He has settled into this side straight away and is doing ever so well on the pitch for us. The future looks bright for him."
Cherries Player HD subscribers can see Eddie Howe's press conference and plenty more reaction post Crystal Palace reaction here