Doncaster completed a league double over the Owls thanks to Chris Brown's first-half tap-in, the striker's eighth goal of the season.
Wednesday started the game brightly but were outworked and, at times, outmuscled by Dickov's physical Rovers outfit.
Dickov said: "I thought our togetherness and character ran right through the team.
"It wasn't the best we've played, by any means, but sometimes you just have to roll your sleeves up and dig out a result. The boys were fantastic.
"I watched them beat QPR in midweek and we knew it was going to be a tough game and we had to weather the storm a little bit early on.
"After doing that though, I thought we thoroughly deserved the three points.
"It's nice to get the three points without playing particularly well.
"Sometimes it's even sweeter when you get them through sheer hard work and determination."
Rovers are on a four-game unbeaten run, which has included three clean sheets and has followed their humiliating 5-0 defeat at Bournemouth earlier this month.
"There were a lot of harsh words said to the players after Bournemouth but it's not just about that," said Dickov.
"We've got players back fit, players back from suspension, and we've been able to pick a consistent team for three games in a row.
"I think that consistency has shown in the way we've played with and without the ball.
"Conditions weren't great today but as long as you keep on working as hard as you can and you keep trying to do the right things, you'll get results."
Wednesday boss Stuart Gray bemoaned his team's quality on the ball and failure to take advantage of their promising start to the game.
Gray said: "When you're on top you've got to score.
"We dominated possession for the first 20 minutes and Leon Best had a great chance to put us ahead.
"It was that sort of game where the first goal would probably end up defining the game.
"We thought Brown was offside for their goal. Maybe they got a lucky break there but far too many of our boys had an off day.
"We had good possession but they picked up more second balls and probably played the pitch better than we did.
"Our final ball was really poor. The quality on the ball let us down.
"We said 'go again' after beating Queens Park Rangers but it was probably a game too far for us."