Nottingham Forest defender Chris Gunter and Watford captain Adrian Mariappa joined for £2.5 million apiece as boss Brian McDermott looked to bolster his squad.
Free agents Danny Guthrie, Nicky Shorey and Pavel Pogrebnyak have also been lured to the Madejski Stadium since the end of the 2011-12 campaign.
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"We have to believe that we are good enough," Roberts told Sky Sports. "We have got some good players who have played in the Premier League before and that is a bonus for us.
"We have got some other good players who may not have Premier League experience but have experience in other leagues. It is an exciting time for everyone at the club.
"When you look at the side you do not know what the starting XI is going to be and that is where you have to be if you are attacking a league as competitive as the Premier League."
The signing of Russia international Pogrebnyak, who spent time on loan at Fulham last season, surprised many following reported interest from more established clubs.
The 28-year-old opted to leave German club Stuttgart but failed to agree terms with the Cottagers, for whom he scored six goals in 12 appearances.
And Roberts admits that he will be faced with plenty of healthy competition for a place in the starting XI up front next season.
"We played two up front last year and hopefully we will continue to do that," he added. "He [Pogrebnyak] is a big name player who has come in and I would like to see myself up front with him.
"But there are other players here like Noel Hunt, Adam Le Fondre and Simon Church and other players who have helped the club be where they are today as well as 'the Pog'. They will want to take their chances, as will I."