But if the pressure rises going into the two-legged playoff round, Arsenal never shows it.
The English club is featuring at this stage for the seventh time in nine years and has won all 12 of its previous matches, maintaining its record of playing in every Champions League group stage since the 1998-99 season.
The biggest name in qualifying, Arsenal has been drawn against Besiktas with the first leg in Turkey on Tuesday.
Clubs from the other top leagues in UEFA's rankings - Athletic Bilbao (Spain), Bayer Leverkusen (Germany), Napoli (Italy) and FC Porto (Portugal) - are also joining in the fourth and final qualifying round that features 20 teams.
Each qualifier will earn a basic 8.6 million euros ($11.5 million) fee, plus bonuses for wins and draws and a share of television-rights money in a near 1-billion euro ($1.34 billion) payout.
Here are five things to know about this week's first-leg games:
BA DANGER FOR ARSENAL
There will be a familiar face to Arsenal in Besiktas' starting lineup at Ataturk Olympic Stadium in Istanbul, which is hosting the game while Besiktas' Vodafone Arena ground is being redeveloped.
Demba Ba is the Turkish team's top striker after his summer move from Chelsea and he has made a good start to his spell in Besiktas, scoring a hat trick to help it to a 5-2 aggregate win over Feyenoord in the third qualifying round.
Ba scored twice against Arsenal in December 2012 in his last game for Newcastle before joining Chelsea.
Arsenal has the greater threats up front, however, with Chile forward Alexis Sanchez moving from Barcelona in the offseason to join an attack that already boasts Olivier Giroud, Mesut Ozil, Santi Cazorla and Aaron Ramsey.
Arsenal started the Premier League with a 2-1 win over Crystal Palace on Saturday
''Besiktas had a convincing result against Feyenoord,'' Arsenal manager Arsene Wenger said, ''and so for us we have the luck to play the first game away.''
Napoli will be hoping for better luck in the Champions League this season ahead of its playoff against Athletic Bilbao.
The Italian side holds the unwanted record of having the most points of any team not to qualify from the group stage, after winning four matches from six and collecting 12 points last year.
However, Napoli still finished behind Borussia Dortmund and Arsenal on goal difference, and dropped into the Europa League.
Tuesday's match at Stadio San Paolo will be the first competitive match of the season for both teams, with the Italian and Spanish leagues yet to begin.
Celtic only made it this far because of an administrative error by Legia Warsaw, and begins its second life in this season's competition at Slovenian team NK Maribor on Wednesday.
Celtic lost 6-1 to Legia in the third qualifying round but the Polish side was punished for fielding an ineligible player in the second leg in Scotland, costing them a 3-0 ''walkover'' loss and putting Celtic through on away goals.
Legia failed with its appeal to UEFA last week, meaning Celtic is free to take its place in the playoffs.
On paper, Celtic was given one of the easier opponents in the draw, with Maribor having only once reached the group stage of the Champions League - in 1999. Maribor lost in the playoff round the last two years.
LEVERKUSEN IN FORM
Bayer Leverkusen is bidding to reach the Champions League for the second season in succession when it plays FC Copenhagen.
New coach Roger Schmidt has been joined by exciting midfielder Hakan Calhanoglu and prolific striker Josip Drmic from Hamburger SV and Nuremberg, respectively.
If Leverkusen gets through, Schmidt will hope to go further than the round of 16, where the side was outclassed 6-1 on aggregate by Paris Saint-Germain last season.
Former Germany striker Stefan Kiessling warmed up for the game by scoring five goals in Leverkusen's 6-0 rout of sixth-tier side Alemannia Waldalgesheim in the first round of the German Cup on Friday.
''It will be quite a different game on Tuesday,'' Kiessling said.
ZENIT IN THE GOALS
Zenit St. Petersburg will look to continue its rich vein of scoring form when the Russian team visits Standard Liege on Wednesday.
Under coach Andre Villas-Boas, Zenit has won four from four to sit top of the domestic league, scoring 15 goals in the process.
Things didn't come so easily in the third qualifying round, however, with Zenit needing two late goals to beat AEL Limassol in the second leg 3-0 and progress 3-1 on aggregate.
Also Wednesday, it's: Aalborg vs. APOEL and Slovan Bratislava vs. BATE Borisov.
Tuesday's other games are: Lille vs. FC Porto, Red Bull Salzburg vs. Malmo and Steaua Bucharest vs. Ludogorets Razgrad.
The second legs are scheduled for Aug. 26-27.