Lambert oversaw three campaigns of success at Carrow Road, guiding the Canaries up from League One and swiftly on into the Premier League, where they finished 12th.
With the Scottish coach now having taken over at Aston Villa, former Newcastle United and Birmingham City manager Hughton has been charged with building on those solid foundations.
Midfielder Howson - signed by Lambert from Leeds United in January and who has been linked with a £4 million ($6.08 million) switch to join his old boss at Villa - insists the Norwich squad can again prove its worth.
"The club has been on the up the last three seasons, and we have to keep up the hard work.
"We still have all the players here and I am sure we can do it."
Howson, who made 11 Premier League appearances after recovering from a knee injury, continued: "The manager points you in the right direction, tells us how he wants us to play, but as players we are the ones who go out there and do it.
"I don't think it is a case of it just being all
"It is about getting a mix between managers and staff, then all helping each other out."
Howson came through the youth ranks at Elland Road to skipper Leeds, before deciding against extending his contract last season.
The former England Under-21 international insists no matter who is in charge, players will always remain focused on delivering the required performances.
"In my short career, I have now had about five or six managers that I have played under, so nothing really changes there," he said.
"I am obviously very grateful for
"But no matter who the manager is, you have to impress every day, so that does not change."
Howson added: "I feel it went reasonably well in the games I played last season, but it helps when you have great players around you.
"Playing in the Premier League is what you dream about when you are a kid.
"My aim now is to have a good pre-season and hopefully get a few more games under my belt for Norwich."
Hughton takes his squad out to
Hughton is expected to bring in at least a couple more fresh faces ahead of the Premier League kick-off at Fulham on
"There might be positions where I feel I don't need to strengthen and there might be positions where, for what's available, I think we have got better here," said the new Norwich boss.
"What I have is a team that has done well with good team spirit.
"I do want to improve the squad, but I have to be very conscious there is a lot of good here and you don't want to remove too much of that."
English Premier League