Newcastle have been eliminated from the FA Cup, League Cup and Champions League. Howe's side are 10th in the Premier League standings after 28 games and still have an outside chance of qualifying for the Europa Conference League next season.
"We have a responsibility in the last 10 games to build. We will always have our targets for the season because we are building for the future and to be the most competitive team we can be," Howe told reporters on Saturday.
"There will be no negativity from me or the players. We know the importance of representing the club well in every game and every single moment."
Asked if qualifying for European football would help salvage the season, the English manager said: "That's our aim. There is a huge amount to play for, people say our season is over and that's absolute nonsense.
"We're driving forward to try to get our best form back and try to win as many games as we can. We aim to finish the season in a positive way."
Newcastle next host West Ham in a league match on Saturday.
