The Robins have lost their way since Smith declared his intention to leave the club when his contract expires at the end of the season.
Smith's men have managed to score only four points in their last three outings, following up a painful loss to Huddersfield Giants in the Challenge Cup semi-finals with a dismal 32-0 defeat at Castleford Tigers.
But Smith believes his players are still playing for him as they prepare to part ways in September.
"They tell me they are and I trust them," said the Rovers head coach, who confirmed Brad Takairangi suffered a significant hamstring tear at Wheldon Road.
"Otherwise it would be excuse making and we're not into excuse making.
"We're low on confidence at the moment, had a big Easter where we worked really hard and have lost a few people since then which has been disruptive.
"Then you go into a couple of games that you really put your heart into and fall short.
"When you're a sportsperson, you understand some of that psychology - it flattens you a bit.
"We're flattened at the moment and I don't think it's down to my announcement; it's down to how we reacted to the last couple of games.
"They care, I care - we all care about it. Rather than try too hard, we just need to get back to building our confidence by working hard on the field."
Sunday's result saw Castleford replace Rovers in the top six, leading to fears among the fans that the club's season is coming off the rails.
Smith can see why supporters are frustrated but reiterated that the loss of form is not linked to his shock decision.
“We're frustrated and sorry we're not delivering better performances," he said.
"We're not shying away from that but I don't think it's down to any announcements.
“They're good boys and would tell me if it was a case that I'm not the right person for them at the moment. They are fine with my decision going forward.
“That’s all we have done - made a decision about what happens at the end of the year to enable the club to find their best-suited coach beyond me.
"The club has done that through the week and that's good. It is good we can sit down and see where our futures lie.
"In the meantime we need to get back playing our confident style of rugby league. At the moment that's just not there for us."