Jordan Rhodes took his season's tally to 15 for Rovers with a header in between goals from Dale Stephens and Yann Kermorgant.
The reaction to the result was an all-too-familiar chorus of boos from the home fans.
"I think the atmosphere in the stadium was a strange one so I think they've got to deal with that," Appleton said.
"They're a big fish in a smaller pond to what they were in last year in terms of the Premier League.
"There's added pressure that goes with that and they're going to have to cope with it because we have three home games coming up in quick succession and it's going to be a challenge for everyone.
"I'm sure the supporters just want to see a committed performance from the players. I think they huffed and puffed today but I'm not sure how committed they were once we conceded the second goal, which was a disappointment.
"There's no time to shirk your responsibilities. We're professional people, whether you're manager, coach or a player. You've got to take the responsibility that goes with it."