The Cherries were 1-0 winners against Tottenham in the Premier League on Thursday.
The result means they are pushing up to challenge for a European position, sitting in 9th place after 14 matches.
Post-game, Smith stated to Amazon Prime: "At home we are a force, even away from home, we press high and we don't care about who the opponent is. Here the crowd gets behind us and our mentality is top.
"It was frustrating that we had a few good chances, especially at the end, and didn't score. Teams like this you have to finish them off. Credit to the defenders though who did fantastically at the other end and it was another great win.
"We have got so many exciting players. The club has done so well in recruiting big talents and we have so many options to come off the bench too. The club is moving forward for sure, we have a new training ground coming, the owner wants to build a new stadium as well. We just need to keep building forward.
"The sky is the limit, for sure. The owner wants to do big things, we have got a great manager as well, it is only positive things going forward.
"After we beat Man City and Arsenal we went to Brentford away and it is teams like that which we struggle with sometimes. We need to get up for those games, especially against the teams in and around us. This league is so tough and it is only getting better, which is scary."
- Get breaking football news faster with the new Tribal Football app! Download now on iOS and Android to stay ahead of all the latest transfers and football updates. Download now: App Store, Google Play