It meant Liverpool, who took fourth spot earlier in the day with a 3-1 win of their own at Bolton, have been pushed out of the top bracket again.
Moyes explained: "Liverpool are still the favourites, they have to be. We have been consistent but for them fourth would be expected.
"We are doing everything we can to make a fight of it, but the bookies are probably right to make them favourites.
"They are looking at the two clubs and where they have been in the past and they are making their decision on who are the favourites in the light of that.
"We have to keep our play at this level and keep going right to the end.
"Our performances are getting better, so all we can do is to put ourselves in a position to keep going forward."
Moyes said: "We showed a lot of character to get this result. Portsmouth are top opposition, they don't lose too many away from home and they are hard to score goals against.
"They all want a European place. Portsmouth are a good side and hard to beat, but I feel we have realised that we can play against the best teams and cause them problems.
"Even with several players down with sickness this week and Mikel Arteta out injured, we have still been able to get a real positive result."