The Three Lions got their World Cup 2014 qualifying campaign off to the perfect start with the 34-year-old's eighth penalty for his country, making him England's most successful ever penalty taker and, with his 24th and 25th goals, 13th highest goalscorer overall.
Despite the Chelsea midfielder not being in his best form, Hodgson decided to put his faith in Lampard because of what he described as his proven quality.
| INTERNATIONALS LATEST
|17/2||Scotland are 17/2 with Paddy Power to beat Serbia 2-1 on Saturday
He told The Guardian: "Frank was excellent. Like Steven [Gerrard], he is a quality player, and quality is permanent.
"That's been proved time and time again. They might not always play at the very top of their game, but you're always better off going into games with that quality on the field."
Hodgson also confirmed that John Terry is a doubt for England's next match against Ukraine after coming off against Moldova two minutes from time with an ankle problem.
"I'd liked to have taken him off [earlier], and we did suggest [to Terry] we'd play with 10 [men]," said the England boss.
"But he's a warrior, though, so he poo-pooed the suggestion he should come off with 20 minutes to go.
"It's obviously not a very serious injury, but every knock is important with only three days between games. But he knows his body after all these years, and he obviously felt it wasn't as big a problem as we feared on the bench. It's very rare, as a coach, do you sit on the bench and winning by four or five and feel you can see the game out with 10 men. It hasn't happened many times in my career. It did tonight."
Despite the injury to Terry, Hodgson was pleased with England's start on their journey towards the 2014 World Cup in Brazil.
"We're very pleased," said Hodgson. "The first match of a group is always a nervous occasion and you're worried you won't produce the performance or the result you want, but we got off to the best possible start. In the end, the scoreline did not flatter us."