Roberts told ESPN: "Today we said we were looking to win the game and look up towards Europe. We don't want to be looking behind our backs.
"It's going to be tough but it's better looking up than down."
The first goal came from £6million signing Nikola Kalinic four minutes before the break, and second-half strikes from Roberts and Gael Givet ensured Rovers claimed their fourth successive home league win.
Roberts said: "That's the key thing - our away form hasn't been great, we need to improve that, but if we can keep picking up points at home we'll be okay."
Rovers manager Sam Allardyce added: "It's our biggest win of the season and we've been threatening for a long time on chances created.
"We had to withstand a bit of pressure from Bolton in the second half but we did that and did it very well.
"We got a clean sheet and three goals and sent the fans home very, very happy.
"We can look up instead of down now and see how high we can finish."
Allardyce was impressed with the contribution from 22-year-old Kalinic, who has taken his time to establish himself in the Rovers team.
"£6million for a frontman is a drop in the ocean today," said Allardyce.
"We decided to go young and invest in someone who can get better and better.
"Niko has come through and said 'I'm worthy of a place in the side'.
"You could see his quality today. I'm delighted for him and I'm delighted for everyone."
With his side's next three Premier League games against Liverpool, Tottenham and Chelsea, Allardyce said: "We can look at those now and we can try and take something from the top end, which would be a bit of cream on top of the cake.
"Anything we can get off Liverpool or Aston Villa or Man United or Chelsea is a bonus for us."
Bolton boss Owen Coyle felt his players were slow out of the blocks.
"First half we didn't get to the performance level we've been at of late," he said.
"I felt we played for 20 minutes of the game at the start of the second half and we could have got the equaliser.
"We'll pick ourselves up and we'll go again."
With no goals scored in their last five league games, Coyle added: "It has to be rectified very soon.
"It's not as though we're not making chances, we made great chances today.
"The boys just have to keep believing in themselves."