The 'Cherries' swept their opponents aside at Vicarage Road as they continued the club's best-ever start to a Premier League season with their biggest top-flight away victory.
Their performances so far see them sitting pretty at the top end of the table, with 16 points from their eight games of the season so far.
Speaking after the game, Howe hailed his side, saying that they are capable of beating anyone on their day, though he also admitted that there is room for improvement.
"I think we're capable of beating anybody when we're on the top of our game," Howe enthused. "I don't think we were on top of our game today, so that's good because there's room to grow and improve.
"But the results show we are in a really good place at the moment, a great position in the league, and we need to keep our feet firmly on the floor and keep pushing.
"Hopefully they won't [start talking about us]. We like to stay very much in the background and as underdogs. We'll just go about our work in a very controlled way and not get ahead of ourselves."
Meanwhile, the Bournemouth boss retained special praise for young playmaker David Brooks, who opened the scoring.
"David is an outstanding young player," Howe went on. "He's come in and looked the part.
"It's great to see him scoring goals and creating goals. All round a very good performance. He's got a very good mentality, which I saw when he first came into the group.
"He's not flashy, not fazed by anything. Just goes about his business in a really good way. Very professional guy. He's got a good future ahead of him."