The England international scored the winning goal in stoppage time for the Three Lions on Thursday night.
"I think he's that important (as Messi and Ronaldo)," Anderton told Sky Sports. "I think they're completely different players of course.
"He is the complete centre-forward, he does everything. He scores goals with his head, he leads the line, left foot, right foot.
"He works hard for the team, he'll go in channels if he needs to. He doesn't get bullied by any centre-backs, he's strong, he knows how to look after himself.
"As a player and having him in your team, he's a dream to play with. Of course a manager's dream as well."