Callum Wilson’s first-half double had put Nuno Espirito Santo’s side on course for a third straight Premier League win, but Bournemouth fought back with two goals in 12 minutes.
The goalkeeper stressed that while the result was frustrating, the team can build on their performance and take confidence from their display in both halves.
“Personally, I'm happy with the performance I've put in today, and I tried to help the team as much as I could, but in another way, it’s frustrating,” Areola told the club website.
“It’s frustrating because I think we started well. The first half was for us, and we managed to score two goals to be ahead.
“After that, it's never easy to play here, and in the second half, they pushed, and they tried to win that game, but we managed to get the point today.
“We knew that they would be pushing and putting pressure on us, but we have to look back and see where we were in the last games.
“We’ve managed to win two, a draw today, and now we have to keep that dynamic and try to get as many points as we can.
“I think we've shown a good picture of what we're doing, what we're trying to do, to be all together, to fight for every single ball and try to win games. We have to keep that positivity and prepare for the next one.”