Hodgson praised Lampard's display, insisting the Chelsea midfielder's "quality is permanent", after the 34-year-old scored twice before the interval to take his tally of goals at this level to 25.
The only concern for the England manager was an ankle injury sustained by Lampard's club-mate John Terry, which saw him reluctantly withdrawn and the visitors play with 10 men for the last two minutes, with the problem to be further assessed over the weekend.
The defender is a doubt for Tuesday's game against Ukraine at Wembley but the injury did not detract from England's encouraging opening to Group H.
"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.
"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."
Lampard had not scored twice in a game at this level since the World Cup qualifying victory over Croatia in 2009. "At my age, you cherish and appreciate wins like this more," said the midfielder. "These can be tough places to come, but the way we started showed our intent. We were comfortable by half-time.
"We are trying to improve and we will need to keep at a higher level for 90 minutes against Ukraine, who are a better team. But going past Hurst's tally was a proud moment. It was an achievement I can look back on with pride."
Hodgson had attempted to withdraw Terry from the fray with about 20 minutes of the contest still to play, the centre-half having taken a kick to his right ankle in the first half and then landing on it awkwardly near the dug-outs after the interval. "I'd liked to have taken him off, and we did suggest [to him] we'd play with 10," said the manager. "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."
There are no concerns over Gerrard, who was rested after the interval, and England still hope to have Ashley Cole available on Tuesday. The full-back trained at Chelsea on Friday and his ankle will be assessed by England's medical team when the squad reconvene at their Hertfordshire base on Sunday. Yet he must displace Leighton Baines from that position to win his 99th cap against Ukraine, the Everton full-back having marked his first competitive staff with his first international goal.
"The win shows what we're capable of," said Baines. "Not many teams would come here and do that. Moldova had a couple of tight games against Holland recently and this proves we've got goals in us throughout the team, players who can score. Not only that, we kept a clean sheet. We could take Stevie off at half-time and it helps when you're not having to over-exert yourself when you've got a game on Tuesday. We'll feel the benefit of that against Ukraine. That's a game we're looking forward to even more now."
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