Wales' now face world champions South Africa on June 5 in Cardiff before Kiwi Gatland returns to his native homeland for a two-Test tour.
But, despite finishing fourth in the championship, British Lions utility back Hook believes the Dragons can compete against the very best in the world.
Hook said: "The win will give us great confidence going into the summer tour in New Zealand.We know we have a lot to work on but we have beaten quality opposition and can build on this.
"It is nice to have South Africa first up and we hope to get a result here before a massive tour to New Zealand.
"We have had a disappointing Six Nations campaign but the games in the summer are all massive. We want to give the players, coaches and supporters what they deserve. We are looking forward to it."
Prior to the clash in Cardiff, Gatland admitted jobs were on the line for himself and his coaching staff following a below-par campaign as Wales set out to avoid collecting the dreaded wooden spoon.
But Hook insists the under-pressure Wales squad will firmly stick together as they prepare for the 2011 World Cup. He said: "We want to do well for the coaches and the team in every game and today was no different. But, to be honest, we do not think about things like that."
Wales welcomed back fit-again Mike Phillips for his first Test start since starring for the Lions in South Africa last summer.And the Ospreys scrum-half, who has been out since October with an ankle injury, admitted his relief following his successful return to the international stage.
Phillips said: "I really enjoyed it. The Lions was a great experience but it was great to be back involved with the squad and team. I have been working really hard and always focussed on returning. I felt really fit and strong. It was important for me to come back and show what I can do. "It was nice to have a start as it has been frustrating watching the Six Nations on television. Playing for Wales is always a dream come true. I wanted to lift the tempo and bring experience to the rest of the lads. We wanted to be positive as a team.
"The first 20-30 minutes were tough but we knew we could break them down. It was nice. It's been frustrating watching the Six Nations and it's great to be involved again. Playing for Wales is always a dream come true."
While Phillips has played a bit-part in Wales' fortunes throughout a mixed campaign, the confident number nine highlighted the frustration of the squad. "It's been a frustrating season for Wales. On the whole the campaign has been disappointing," he said.
"But it's nice to finish on a high with some confidence and great to get a win. We can build for the summer tour but before then we will get up for the rest of the season.
"The Ospreys have a big European game at Biarritz and that's the next big one for us. We need a big performance and perform well before the tour."
Italy finished bottom of the table following Scotland's shock win against Ireland at Croke Park. Italy captain Leonardo Ghiraldini said: "It's been a great honour to lead the side in Sergio Parisse's absence. "We have got a good bunch of players and it was a great pleasure to lead the side.
"We were disrupted this week with injuries and we lost even more players during the game. But I'm proud of the way we defended as a team."