Former England striker Beattie took over in the summer as manager after Stanley only avoided relegation in the final games of last season.
And he feels his new-look side will go places after picking up their first point of the season against Pompey, where Peter Murphy and David Connolly both scored twice to ensure the shares were spoiled.
"I think we are stronger than last season, maybe the numbers have come down but the quality has gone up," said Beattie, who had winger Kal Naismith from Rangers making his debut at the Crown Ground.
"We need to add one or two more players and look at the loan market which is something I am working on at the moment.
"Some of the lads played well and some were below par and they are disappointed. I am not a manager to shout and scream but sometimes silent treatment is worse. I found that from my dad if I hadn't played well.
"But we have a great togetherness and a team spirit and we will build on this. I felt Portsmouth were there for the taking before the game but, at the end, I have got to be happy with a point."