Newcastle's return to the top flight was confirmed before they kicked a ball against Sheffield United on Monday night after Nottingham Forest failed to beat Cardiff, but the squad are determined to finish the season in the position they have held for the majority of the season.
Smith revealed the team would be disappointed if they weren't crowned champions.
Smith said: It's not finished yet. We're pleased with promotion and the manner in which we have achieved it, but we wanted to go up as champions at the start of the season and that is what we need to make sure of over the next five games.
We've come this far and it would be disappointing if we didn't win it now. That's the feeling inside the camp and it will keep us going this season.
We've also got an unbeaten home record to maintain.
With visits to strugglers Plymouth and QPR still to come between now and the end of the season, Smith claims the team will not relax until the title is theirs.
There are clubs out there fighting for their lives over the next five games and we want to win the title so we won't be taking it easy, said Smith, who has started 28 of the Magpies 41 Championship games this season.
The former Manchester United and Leeds strikercum- midfielder also revealed that despite some thumping victories at St James' Park this season, it's the scrappy one-nil wins away from home that have been just as important.
People say it's the hardest in the world to get out of and we've done it. We have respected our opponents and we've had some really tough battles every game we have played, he said.
Every game has been hard, bar a few, the 1-0 away wins at Preston, Cardiff and Sheffield United, they stick out when you look back.
The 1-1 draw at Swansea on the back of a defeat at Derby, these were crucial games. If you're not 100 per cent, if you're not focused, this league will punish you. If you take your foot off the gas it will hurt you.