The Gunners saw their European aspirations ended at the last-16 stage once again despite Tuesday night's 2-0 victory in Monaco, which saw them go out on away goals.
Despite all of their success in qualifying for the group stages, it is now five seasons in a row that Arsenal have failed to reach the quarter-finals of the Champions League.
Manager Arsene Wenger lamented the costly 3-1 home defeat in the first leg last month, when a breakaway stoppage time goal proved fatal just moments after Alex Oxlade-Chamberlain had scored what should have been a lifeline.
Centre-back Mertesacker, who captained the side at the Stade Louis II Stadium, accepts Arsenal cannot afford such lapses in concentration if they are to compete with Europe's elite clubs on a consistent basis.
"In the first game, we didn't have that mental level you need to compete at the highest level
That was missing but you could see on Tuesday night in Monaco how good we are as a team and how well organised we can be," the German World Cup winner said.
"We need to consider that every day in training and in games, that is why we are so far away from winning the Champions League.
"It is the last 16 and Monaco were underestimated by a lot of people, but they deserved it by playing well in the first leg.
"We had one bad game and that is enough to get knocked out.
"In the first leg, we conceded that late goal which was overall the killer, so it is really disappointing for us."
Arsenal almost upset the odds in the principality tax haven, famed for its casinos and yacht-lined waterfront.
Despite having come up just short in their historic bid to qualify from such a first-leg deficit, the Gunners remain in good overall form.
The victory in Monaco, who had not conceded a goal at all during the Champions League group stages, was a 15th win from the last 18 matches in all competitions.
Arsenal are into the semi-finals of the FA Cup at Wembley and could yet have a say in the Barclays Premier League title race, as they are now just a point behind second-placed Manchester City.
Aaron Ramsey, who scored a second goal on 79 minutes to pile on the pressure after Olivier Giroud's first-half opener, is confident for the challenges ahead.
"We could take some positives from the Monaco performance and hopefully we can get back on track against Newcastle this weekend and we can keep that running run we are on," the Wales midfielder said.
"Many things can happen in the Premier League still, with many twists and turns.
"We will be looking to concentrate on ourselves and take full advantage of the games we do have left.
"We are also in a good position in the FA Cup
We have Reading (in the semi-finals), which we will feel confident of going through."
Monaco, meanwhile, are through to their first Champions League quarter-final since 2003/04.
Coach Leonardo Jardim accused Arsenal of being "disrespectful" to them at the Emirates Stadium, where Wenger did not accept his offer of a post-match handshake and so decided to snub the Frenchman at Tuesday's full-time whistle.
Veteran striker Dimitar Berbatov felt Monaco's team work ethic was key to their victory.
"I don't think anyone expected us to be in the quarter-finals, but we always felt we could do something special," the 34-year-old former Tottenham, Manchester United and Fulham forward said to www.uefa.com.
"Our team is very young, we have some great talent and, as you could see, we surprised many people.
"We qualified against a strong Arsenal side, we fought as a team, had a bit of luck, but in the end we got through.
"The last 10 minutes were very nervous as Arsenal were looking for their final goal, but we fought and everyone gave 100 per cent to hold out so we could qualify."
Source : PA
Source: PA