Liverpool's Luis Suarez and Chelsea defender John Terry were both handed bans for racist abuse in the last 12 months.
"I think most of us would be worried by the recurrence of the issues around racism in football," Robertson told Radio 5 Live's Sportsweek programme.
Asked if the Football Association, who suspended Terry for four games, should have been harder on the England captain, Robertson added: "Yes, I think in retrospect the answer to that is yes.
"They are in a difficult position because they have to follow the law and there are legal challenges on all sides, but I don't think anybody looking back on this year would think it's been a particularly happy chapter.
"By the same token, and my guess is that (UEFA president Michel) Platini himself feels that, I think there's widespread feeling in the game that the penalties dished out to Serbia (following the Under-21 match against England in October) were not tough enough either.
"It's one of those things racism that you've really got to keep on top of it the whole time.
"I've seen quite a few black players who've asked to come and see me to talk through the problems. They very clearly feel there aren't enough black coaches, there aren't enough black managers, there's a glass ceiling on top them.
"That's why developments like St George's Park are going to be so important to bring through a new generation of black coaches and black managers to try and tackle this.
"Just look at the FA council, and ask yourself how many ex black players and how many women there are on that body, it's not a great advertisement."