FC Barcelona's victory against Arsenal FC and passage into the UEFA Champions League quarter-finals seemed intense and nerve-wracking to the neutral observer, but Josep Guardiola's players believe the result – 3-1 on the night, 4-3 on aggregate – was never in doubt.

Their faith in the trademark Camp Nou playing style and the footballing genius that Lionel Messi appears to produce at will on the big occasion was enough for Daniel Alves, Xavi Hernández and Pedro Rodríguez to feel relaxed about the fact that just one slip and one more away goal for Arsenal would have sent the Gunners through instead.

"Perhaps this was our most difficult game so far in the Champions League this season but we have Messi and he's on a superior level to anyone else," right-back Daniel Alves told UEFA.com. "He's our genius, the guy who pulls us through tough games and he's done it again. He wasn't alone, we all know that Messi was accompanied by a great team tonight but he's the perfect complement to our work."

It was Messi who turned the tie. Just when Barcelona looked like they might be blunted by Arsenal's substitute goalkeeper Manuel Almunia, the Argentinian No10 danced round the Spaniard from an Andrés Iniesta pass and scored in first-half added time to settle whatever nerves there were.

Even a Sergio Busquets own goal eight minutes after the break failed to shake Barça's composure. After the 56th-minute expulsion of Arsenal forward Robin van Persie, Xavi's cool finish followed by a converted Messi penalty served to eliminate an Arsenal team who had one brief late chance against the run of play – Javier Mascherano denying substitute Nicklas Bendtner with a wonderfully timed challenge – to wrest an unlikely victory.

Midfielder Xavi, the Barcelona captain, told UEFA.com: "We were superior to them from start to finish. We imposed our football, we remained totally loyal to our manner of playing – we demonstrated our personality. Arsenal barely had a shot on goal and their only goal was scored by our player. They didn't want the ball and our tempo of play and our intensity was always going to see us through."

Now, for Barcelona at least, the rest of the tournament beckons. The draw is not seeded so a tie against Real Madrid CF in the quarter-finals is a possibility should the capital club knock out Olympique Lyonnais next week. That would mean four meetings – the sides are also due to play in the Liga and contest the Spanish Cup final – in just over a fortnight.

"It's true that Real Madrid might be our next opponents but there remains a wide range of teams we could face," said forward Pedro. "But all we wanted was to be in the last eight and if fate puts us up against Madrid then we'll prepare for it the same way we would any other club. As for Messi, well I'm all out of adjectives to describe his excellence."