"I did notice the praise Arsenal were getting earlier in the season but it didn't really bother me," Giggs told The Sun newspaper.
"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.
"You find that every team you come up against in the Premier League is playing for something, whether it's battling to stay up, going for a place in Europe 'or trying to win a title.
"Many of those clubs would consider a point against United to be a good result, so you're coming up against sides that maybe don't intend to win.
"They just want to defend and get men behind the ball and that's what we'll have to try to overcome - teams that are trying to stifle our play."