The hosts made it four wins from as many matches to maintain their grip on Group E, but were made to sweat as a drab contest burst into life after half-time.
Slovenia restricted England to a diet of half-chances before Jordan Henderson headed into his own net to hand them a 1-0 lead.
England's response was instant as Wayne Rooney won and converted a penalty to fittingly mark his 100th cap before Danny Welbeck netted a double to take his qualification goals tally to five.
"It was not going to be an easy game ever because they were disciplined and well organised," Hodgson told ITV.
"We had a lot of possession in the first half. We were probing but we weren't really getting beyond them and creating the number of chances.
"When we went a goal down it was very, very important to break straight back.
"We did with the penalty and after that our play was certainly better. I thought we created a lot more chances.
"In the end it proved to be a very good victory because we've seen today that Slovenia have been good value for their six points and their two victories so far.
"Now, in the group, we've beaten Switzerland away and Slovenia at home, which puts us in a good position."
That good position amounts to a six-point lead and Hodgson felt the manner in which his team kept their composure amid their first-half struggles was vital to securing such a healthy advantage.
"I thought we kept our shape well all the time, even when we weren't playing our best football," he said.
"We won the ball back quickly and sustained attacks, but it was really frustrating that we weren't creating the chances that our ball possession could have given us.
"In the second half I thought that was better. The chances were coming one after the other and it gave us three goals, which was more than enough to win the game."
