A shock failure to reach the group stages of the Champions League cast a shadow over Udinese's hopes of making a bright start to their domestic campaign, with the club struggling to claim a solitary point from their first three Serie A games.
It was Portuguese side Braga who edged a place at Europe's top table thanks to a penalty shoot-out triumph at the end of August, with an angry Guidolin immediately threatening to resign after just two years in charge at the Stadio Friuli.
But after being convinced by the club's board to remain in his role, the former Parma boss is determined to make amends and return his side to winning ways.
He said: "We are always in the hunt for victory, but it is never easy to win.
"We are not performing as we should be and now we are faced with more strong opposition."
For Guus Hiddink's Anzhi, a first shot at the Europa League group stages represents just the beginning of a projected assault on continental competition for the big-spending Russian outfit.
Hiddink can call on a host of international stars, including Samuel Eto'o, Yuri Zhirkov, Christopher Samba and Lassana Diarra, but Guidolin believes Anzhi's sheer ambition will make them a force to be reckoned with.
He added: "It's not all about Eto'o, they've got a lot of valuable players.
"They are a team that wants to become very important on the international scene. They have great strength in depth and are a good team.
"They're a team that plays 4-4-2, who are coached by a great coach and that can be very adaptable."
Anzhi arrive in Italy fresh from a 5-2 victory over FK Krasnodar in the Russian League, in which Cameroonian striker Eto'o, formerly of Inter Milan and Barcelona, scored twice.