Norwich have impressed on their return to the top flight, and Whitbread, 27, feels an extended cup run would sit well alongside Norwich's battle to last the distance in the Premier League.
"Without a doubt the league is the main focus, but the FA Cup are games where we will always give 100%," Whitbread said.
"After the league win over QPR last week, there could have been some heavy legs, but with the matches churning out thick and fast, it is good to get into that momentum.
"If you are playing in those games, you don't really want to stop and have a long break - you want to keep the ball rolling."
Whitbread continued: "We now have chalked up two wins on the bounce, which does us no harm.
"It is always good to get on little runs, because winning breads confidence.
"Hopefully that carries on into West Brom next week.
"We have just to keep working hard, approaching games right and then the results will come."
Lambert had opted against making sweeping changes to Saturday's starting XI, as he maintained the same back four which played in the win at Loftus Road with Declan Rudd deputising in goal for new dad John Ruddy.
It proved a positive move as the Canaries raced into a 2-0 lead through Grant Holt and Simeon Jackson, before Burnley reduced the deficit when Jay Rodriguez looped in a header.
Holt then missed his first Norwich penalty on 31 minutes after what looked a harsh handball decision against Charlie Austin.
However, the home side resumed command of the tie in the second half when Andrew Surman swept home on the hour before substitute Steve Morison tapped in number four from close range just minutes after coming on.
Norwich have surpassed many expectations already, but Lambert knows bigger tests await between now and May.
The Scot has already handed the Norwich board his list of transfer targets, but accepts getting them to Norfolk may prove more testing.
"I am not so sure [we can make the signings]," Lambert said.
"I know who I want, but we can only do what we can do.
"I can't bring the wrong people to the club who I think will just be a squad player, you want them to come in to prove it and give the lads a hand.
"That is the frustrating thing, but that is the same for every team."
Burnley were stretched in defence by the suspension of Kieran Trippier and injury to Michael Duff, while midfield duo Marvin Bartley and Keith Treacy had both been laid low with a virus and were only included on the bench.
Clarets boss Eddie Howe believes the Turf Moor club - who were in the top flight themselves just a couple of seasons ago - can take heart from the recent achievements at Carrow Road.
"We have to look at Norwich as our role model, really. We want to emulate them and the success they've had coming from League One," said Howe, whose side are just three points outside the Championship play-offs.
"Their team spirit is something that really stands out, so there's a lot of things to look at and say 'that's the route that we want to take'."
Howe added: "We competed as best we could at Norwich, but now have to turn our attentions to Middlesbrough and make sure we continue our good league form because hopefully we will have a lot to look forward to in the second half of the season."
