Wayne Rooney - making his first appearance as full-time England captain - scored the only goal of the match from the penalty spot in the 68th minute after Raheem Sterling had been felled by Omar Elabdellaoui in the box.
The strike - Rooney's 41st in an England shirt - put the gloss on what was an otherwise unconvincing display, but Hodgson believes his side deserved the victory at a half-empty Wembley.
"We probed very well in the first half and asked a lot of questions of them," he told ITV.
"I thought we started the second half poorly. I was disappointed with our first 10-15 minutes at the start of the second half.
"[England goalkeeper] Joe [Hart] had to make a couple of saves having been pretty much a bystander in the first half, but luckily we got ourselves going again.
"With the injection of Danny Welbeck, Fabian Delph and James Milner and the slight change of the system I think we got back on top again and started to create chances.
"In the end, I thought we were good value for our victory."
Hodgson handed a first England start to Everton defender John Stones, while Delph and Calum Chambers came off the bench for their debuts.
And the 67-year-old is encouraged by the depth of quality he has at his disposal.
"I think it's good that we have these options," he added.
"I thought we definitely changed the way we were playing in terms of the system quite radically with about 20-25 minutes to go and I thought that worked well too.
"When Welbeck came in alongside [Daniel] Sturridge and Raheem played in behind them, we got that going as well.
"In the end, with a little bit of luck, we'd have aggravated the score, but the important thing was the victory."
England begin their Euro 2016 qualifying campaign in Switzerland on Monday.
