Arsenal may have left Munich with their heads held high after ending Bayern's 23-game unbeaten run, but they mustn't get carried away by their 2-0 Champions League win, Graeme Souness told Sky Sports.
After being outclassed by the German giants in the first leg, the Gunners produced a much-improved display at the Allianz Arena.
Olivier Giroud's strike on three minutes gave them hope and Laurent Koscielny's header in the closing stages set up a grandstand finish but, despite a determined effort, they were just unable to overturn their first leg 3-1 defecit and crashed out of Europe's premier club competition on away goals.
However, despite the visitors almost pulling off a remarkable fightback, Souness pointed out Bayern had been well below their best and Arsenal still have a long way to go if they are to come out on top against Europe's best on a regular basis.
"Although on the face of it 2-0 looks fantastic this was a shadow of the Bayern Munich we have come to expect to see," the former Liverpool midfielder told Sky Sports.
"Arsenal will be looking back at the first game and thinking 'if only we didn't concede three goals' but if they had only lost 1-0 at the Emirates, would we have seen the same attitude from Bayern that we got here? I don't think so.
"We thought Bayern would come into this game with their tails up and win at a canter but they started slowly and when they conceded the early goal they were stuck between two stalls and didn't know what to do.
"Bayern looked like an ordinary team - but did Arsenal work Manuel Neuer all night and force him into save after save? No. So I'm thinking Arsenal won 2-0 without being special.
"Defensively Arsenal were fabulous which they have not been this season but, although I don't want to take anything away from them - because they came into this game under lots of pressure - Bayern were not at their best."
However, Jamie Redknapp felt the result, although not enough to prevent Arsenal crashing out of the Champions League, can at least instil some confidence in the Gunners' for the rest of the season, as they chase a top four spot in the Premier League.
And the former Liverpool and England midfielder applauded the London side's defence for keeping out Bayern's potent attack.
"None of us gave Arsenal any hope whatsoever but they were magnificent," said Redknapp.
"It was a great performance and they will take a tremendous amount of pride from that performance. A clean sheet and a win here against one of the real contenders in this tournament was excellent.
"Arsenal stopped them playing with any pace and they defended a lot better.
"Koscielny was the man of the match for me. With Thomas Vermaelen and Per Mertesacker there is a real lack of pace, but Koscielny gives them an injection of speed and whenever the ball is played in behind he can react.
"He has a great ability to read situations and was immense."