The Minstermen host strugglers Bristol Rovers this weekend before a visit from league leaders Gillingham seven days later.
A run of three straight defeats resulted in some travelling fans venting their anger towards the team and management at Plymouth last weekend.
But Smith is aware all at the club need to pull together to see the Minstermen over the hard times.
He told The Press: "At the end, we were going over to clap them and thank them (the fans) irrespective of the result.
"There were a few booing and some fans were shouting stuff at certain players, management and staff. If that's what they want to do, but some of the verbals were a little harsh."
He added: "They have every right not to be happy with the performance and we wanted to thank them for making the effort.
"They had probably spent a lot of money and I know it's disappointing for them, but we feel it as well."