Isak struck in the 57th minute for his fourth league goal of the season, reacting quickly after Cody Gakpo's cross caused problems in the Bournemouth defence.
The Sweden international has already scored more Premier League goals in Liverpool's opening five matches this season than he managed throughout the whole of the previous campaign.
However, Iraola believes Isak can contribute more to Liverpool's overall attacking play.
"He took the chance after a quiet afternoon - and that's what a striker's job is like," Iraola said.
"He had a couple of situations, a cross he didn't hit properly, one when his control wasn't right and then the goal.
"But he has to help us to be closer to the box, to play in the opposition half and to have meaningful possession.
"Then, if the team is playing there, he will receive the rewards in terms of goals. We need that level so that we can play better."
The victory was a significant one for Iraola on his return to Bournemouth, where he spent three seasons before moving to Liverpool after guiding the Cherries into Europe for the first time.
Liverpool struggled to impose themselves during the opening stages, despite having two extra days of rest compared with Bournemouth following the hosts' Europa League victory over Real Sociedad on Thursday.
Iraola admitted he was unhappy with Liverpool's start.
"I was disappointed with the first 20, 25 minutes. I think we didn't start the game with the intensity it requires," he said.
"To win here is very difficult, I know it very well. Normally Bournemouth starts really strong, and it took us this 20, 25 minutes until we matched a little bit this level.
"From there I think at the end of the first half and the second half we played better. Better situations with the ball, and we could win the game."
Isak's goal ultimately settled the contest, but Iraola's message was clear: Liverpool need more from their centre-forward and must turn their periods of control into a greater attacking threat.
Liverpool's next men's match is against Manchester City at Anfield on Sunday, October 11.
