The unbeaten north London team strode seven points clear of champions Manchester United with their 2-1 victory at Chelsea on Saturday but their French captain is well aware that last season Arsenal squandered an eight-point lead to finish runners-up.
"Of course we have put ourselves in a comfortable position but last year we learned a lot and we are going to try not to make the same mistake," Vieira told Sky Sports television.
"Maybe (we had) too much belief and too much confidence, going to games and thinking we were going to win easily."
"It is not the case, we know how difficult it is to perform and to win games and I think we are going to be tough to beat this year."
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At the end of the game, with victory secured by strikes from Vieira and Edu after Eidur Gudjohnsen had given Chelsea the lead after only 27 seconds, the Arsenal players huddled in the centre of the pitch in a show of determination and unity.
Chelsea's impressive stadium is unusual in that the away fans populate the area either side of the players' tunnel, which meant Chelsea left the field to boos while Arsenal's players were acclaimed like heroes.
REYES RESTED
Symbolically Thierry Henry, who had been kept quiet by Chelsea's best player John Terry, clutched the badge on his shirt and beat his fist against his heart to show just how much their third 2-1 victory over Chelsea this season meant.
Manager Arsene Wenger refutes comparisons with last season and he knows that the clash at Highbury with United on March 27 could prove decisive.
Last season the equivalent fixture took place on April 16 and United's 2-2 draw proved a psychological turning point.
"It's not a similar position to last year at all because we were never seven points ahead of anybody last year," Wenger told reporters.
"The maximum was five, or eight with one game in hand for our opponents, so that is completely different."
"We didn't make many mistakes, Manchester United had an outstanding run."
On Saturday Wenger was able to rest new Spanish signing Jose Antonio Reyes, scorer of both goals in Arsenal 2-1 FA Cup fifth round win over Chelsea last Sunday, no doubt with Tuesday's Champions League trip to his native Spain in mind.
While Arsenal can approach their second round, first leg match against Celta Vigo with confidence, Chelsea's ego has been pricked by successive losses to their London rivals.
Head coach Claudio Ranieri, whose team is nine points behind Arsenal, awoke to predictable headlines claiming he is about to be sacked by big-spending Russian owner Roman Abramovich.
For now talks of his imminent departure is premature, although should Chelsea fail in their own Champions League quest against VfB Stuttgart, starting with the first leg in Germany on Wednesday, it may not be.
"The Champions League is like a bingo," Ranieri said on Saturday. The Italian badly needs to hit the jackpot.