United have taken just a point from their last two league games, allowing Arsenal to pull five points clear at the top of the table, but Giggs remains confident, despite the acclaim their rivals have had for their stylish football.
"I did notice the praise Arsenal were getting earlier in the season but it didn't really bother me," he said.
"Arsenal were playing good football, but we felt we were as well.
"I just thought, 'Right, you keep talking about Arsenal, put the pressure on them and keep saying that Arsenal have won the league already and that they're going to walk it'.
"It's always been the United way to try to win with good football but our ability to win ugly as well has been a trademark of the last 15 years or so.
"In the majority of games, we're going to try to play attractive football and score lots of goals but we also need the added steel for games like the ones at Liverpool this season and last.
"We did not play particularly well in the last two games at Anfield but still managed to sneak a win. They are the kind of results that really do win leagues, not the big wins like 6-0 against Newcastle."
Defender Rio Ferdinand, meanwhile, believes beating Arsenal would be the perfect way to get United's season back on track.
"It was a very bad weekend," he said, referring to United's 2-1 defeat to Manchester City.
"We've all been thinking about the reasons why it happened and how we want to pull ourselves together and get the result out of our minds.
"The best thing you can do is to come into training and just get focused on winning the next game, and that's what we're doing."
Arsenal's trip to Old Trafford dominates the weekend's fixtures, with Liverpool and Chelsea both facing home games against lower-league opposition.
Chelsea are home to Huddersfield, with midfielder Michael Essien insisting they could yet complete a clean sweep of Premier League, Carling Cup, FA Cup and Champions League.
"We're still in all four competitions and we will do everything to win as many of them as we can," he said. "We have the right character."
Liverpool host Barnsley knowing the FA Cup is their one chance of winning domestic silverware. "I love these big Cup tries," said midfielder Javier Mascherano.
"I just want to win something this season."
Also Saturday, the last remaining League One side, Bristol Rovers, face Championship side Southampton for a place quarter-finals while Cardiff take on Wolverhampton Wanderers and West Bromwich Albion welcome Coventry.
On Sunday, Preston play Portsmouth and Middlesbrough travel to Sheffield United.