Alexis has been one of the most high profile signings this summer following his arrival from Barcelona and his experience in the competition could be vital according to Campbell.
In an interview with Goal, Campbell said: "It is important to bring in players like Alexis who have played in and won [big games] in the Champions League.
"Alexis understands the tournament. We have been there a number of times in the Champions League and it is all about every year being in the game and pushing hard.
"We just need that bit of luck to go our way but you also have to put your neck on the line and buy players – which we are now. You need to be in it to win it and that is what Arsenal are trying to do.
"They are not spending crazily everywhere but if someone comes up they are now prepared to go for it."
Arsenal's record in the Champions League in recent years can be summed up by last season in the competition. They have shown they are capable of mixing it with difficult sides having got out of a difficult group last season involving Borussia Dortmund, Napoli and Marseille but came up against difficult opposition in the knockout stages where they were beaten by defending champions Bayern Munich in the knockout stages.
Alexis is a player who is accustomed to his side being at the business end of the competition and is used to the expectation of being part of a side that is expected to be in contention to win the competition, having signed for Barcelona after they were crowned European Champions in 2011.
In the last four seasons, Arsenal have been knocked out at the round of 16 stage, and will be hoping their summer business will aid them to go further into the competition - with a positive result against Besiktas in Istanbul this evening crucial.