Bajevic, the most successful club manager in Greek football history, sees a chance for his side to grab a vital advantage.
The 62-year-old said: "Everton are a very good side, when they have all their players fit. Then they are strong in defence and midfield. But we are aware of their problems."
Victor Anichebe, Mikel Arteta, Tony Hibbert and Phil Neville are out. John Heitinga is ineligible for Europe.
"We do know and accept that they are one of the best teams in England. Their league position and FA Cup final appearance last season proves that.
"It will be a very difficult game for us. In England matches are very quick, but we believe we can handle that."
Bajevic dismissed suggestions that AEK will only defend at Goodison Park.
"People expect away teams to defend and try to hit teams on the break.
"But we will want to play our normal game. As this is an away game we really have little to lose so we will go for the win and hope to take an advantage into the rest of the group matches.
"I suppose any away team would be happy with a draw, but let's see how the game goes. We do not just want to defend, but we know we will need strength and speed."
AEK'S GREATEST EUROPEAN ACHIEVEMENTSUEFA Champions League-1996-97, Quarterfinal, eliminated by Paris Saint-Germain (0-0 in Paris, 0-3 in Athens)
-1997-98, Quarterfinal, eliminated by Lokomotiv Moscow (0-0 in Athens, 1-2 in Moscow)
Europa League / UEFA Cup-1976-77, Semifinal, eliminated by Juventus (1-4 in Turin, 0-1 in Athens)
Landmark gamesChampions League / European Cup1971-72 AEK Athens - Inter 3-2
1978-79 AEK Athens - Porto 6-1
1989-90 AEK Athens - Dynamo Dresden 5-3
1992-93 AEK Athens - PSV 1-0
1994-95 AEK Athens - Rangers 2-0
1994-95 Rangers - AEK Athens 0-1
2002-03 AEK Athens - Real Madrid 3-3
2002-03 Real Madrid - AEK Athens 2-2
2006-07 AEK Athens - Milan 1-0
Cup Winners' Cup1976-77 AEK Athens - Derby County 2-0
1976-77 Derby County - AEK Athens 2-3
Other notable records-AEK Athens is the only Greek club to have participated in the quarter-final round of all the major European competitions.
-AEK Athens is the only Greek club to have reached the semi-final round of the UEFA Cup (1976-77).
-AEK Athens is the only Greek club to have participated in the group stage of the UEFA Champions League without losing a single game (2002-03).
-AEK Athens is the only Greek club to have advanced to the last 16 of the UEFA Cup in 3 consecutive seasons (2000-01, 2001-02, 2002-03).
-AEK Athens is the only Greek club to have advanced to the last 16 of the UEFA Cup Winners' Cup in 3 consecutive seasons (1995-96, 1996-97, 1997-98).
-AEK Athens is the only Greek club to have advanced to the last 16 of European Competitions in 4 consecutive seasons 1995, 1996, 1997, 1998.
-AEK Athens is the only Greek club to have participated in a European competition's quarter-final round in two consecutive seasons (1996-97, 1997-98).
-AEK Athens is the only Greek club that participates in European Competitions for 22 consecutive years (1988-2010), excluding the season 1990-91 when was punished by UEFA.
-AEK Athens is the first Greek club to have reached the quarter-final round of the Champions Cup (1968-69).
-AEK Athens is the first Greek club to have participated in the group stage of the UEFA Champions League (1994-95).
.
