Allardyce said: "It was a fantastic day for us and a very important three points.
"It's our biggest win of the season and four wins on the trot at Ewood Park. We're making everyone sit up and think what a game they're going to get here - and they certainly are."
The match was not without alarm for Allardyce, with Wanderers enjoying a rare spell of pressure during a heavy snowstorm early in the second half with the score at 1-0, and Allardyce hailed the importance of Paul Robinson's excellent save from Chung-Yong Lee.
But Junior Hoilett and Steven Nzonzi could have extended the lead before Roberts' scruffy goal, after which point Allardyce could relax once more.
"It was a difficult game," he admitted. "One; because of the weather, and two; it's a local derby.
"But we deserved a 1-0 lead in the first half. We then sat back on that a little too much and Bolton had their best spell and threatened that they might get something.
"But when the best chance of the game for them came we've got Paul Robinson, who made a match-winning save.
"Then we got the biggest snowflakes you've ever seen in your life - I was struggling to see the ball and the players almost, they were that big!
"Once we'd weathered that storm we had Junior Hoilett, with a diving header that Jussi (Jaaskelainen) saved, and Steven Nzonzi with the header, and I was wondering if and when the second goal was going to come.
"But when we got that it knocked the stuffing out of Bolton and we just opened them up if and when we saw fit. The third goal went in and it could have been four in the end, perhaps five."
Bolton manager Owen Coyle offered no excuses after admitting his players came up short of expectations at both ends of the field.
He said: "I was disappointed with our performance today. It's no excuse to say you've played a lot of games, we still expect better that what we offered today.
"I think there was a 20-minute period at the start of the second half where we looked like ourselves and could have had an equaliser.
"We had bits and pieces in the first half, which I thought was quite scrappy. Matt Taylor probably had the best chance of the first half and it was a good save.
"We paid a heavy price and the goals we lost, I wouldn't expect to lose those goals in the school playground.
"There were two Blackburn players in offside positions for the second but they didn't affect the goal and Sam Ricketts was certainly playing Roberts onside, the goalscorer, so there's no argument there from my point of view.
"The third goal, we've allowed a short free-kick to be taken and put no pressure on the ball.
"That was really disappointing given how well we've been defending of late - and obviously not scoring, given the opportunities we had.
"When you do those two things well, you get results and points, and we didn't do that well enough today, it's as simple as that."