Real were handed a relatively easy group in Thursday night's draw, where they were pitted against French Ligue 1 outfit Lyon, Dutch Eredivisie champions Ajax, and Croatian outfit Dinamo.
And while many have identified Dinamo as the weakest side in Group D, Butragueno believes Real's visit to Zagreb, which will be followed by home games against Ajax and Lyon could go a long way in determining how well Real do in the Champions League this season.
"If we can get a good result there [Zagreb], after these three matches perhaps we will be in a privileged position to progress [to the next round," Butragueno said, after the Thursday's draw.
"The first match in Zagreb will be key."
Real will also get another chance to lock horns with Lyon, whom they have played against regularly in recent seasons, and Butragueno is aware of the threat the French outfit pose.
"The truth is that it is hard for us at Lyon and we have never won there.
"They are a team with a solid defence, a mature and competitive team and, in that sense, they have never been the easiest opponent."
Real will also face another familiar opponent in Ajax, having played the Dutch champions in last season's group stage as well.
However, despite claiming two victories over Ajax last term, Butragueno is not ready to underestimate them just yet.
"They [Ajax] are a team who have improved and that, despite selling Luis Suarez [to Liverpool], ended up winning their league while playing very well towards the end of the season."
Real's opening Group D encounter against Dinamo Zagreb will take place on September 14.
Champions League Group Stage
|Group A||Group B||Group C||Group D|
|Bayern Munich||Trabzonspor||Manchester United||Olympique Lyonnais|
|Manchester City||LOSC Lille||FC Basle||Dinamo Zagreb|
|SSC Napoli||CSKA Moscow||Otelul Galati||Real Madrid|
|Group E||Group F||Group G||Group H|
|Valencia||Arsenal||Zenit St. petersburg||BATE Borisov|
|Bayer Leverkusen||Olympique Marseille||Shakhtar Donetsk||AC Milan|
|Racing Genk||Borussia Dortmund||APOEL||Viktoria Plzen|