Jurgen Klopp's side sealed top spot in the final round of games in Group D by virtue of a better goal difference over Arsenal, but Dortmund midfielder Sahin was disappointed not to sign off with a win.
Ciro Immobile's 58th-minute opener was cancelled out by Aleksandar Mitrovic's equaliser six minutes from time.
Ultimately, though, the draw did not end up costing Dortmund, although Sahin felt the hosts should have gone in search of victory.
"We are happy, but if we would have been more clever we would have won this match, because Anderlecht didn't look as if they really wanted to score a goal," said the 26-year-old, who returned to the Dortmund starting line-up for the first time since the DFB-Pokal final in May.
"We have to blame ourselves for this draw."
Dortmund were the better side, creating far more chances than their opponents, but struggled to find a way past an in-form Silvio Proto in the Anderlecht goal.
However, in the absence of Mats Hummels in central defence, Klopp's men looked vulnerable at the back and were made to pay when Mitrovic scored from only Anderlecht's second effort on target in the match.
Defender Kevin Grosskreutz criticised Dortmund's performance, but was pleased to see the likes of Sahin returning from injury.
He said: "We didn't play a good match, it took a long time until we came into this match, but we had a lot of changes before this match.
"I am happy that we have many players coming back from injuries right now."
Dortmund have struggled domestically, with Friday's 1-0 win over Hoffenheim just their second win in 11 in the Budesliga.
However, Dortmund have performed much better in Europe and finish the group stage with 13 points and a record of four wins, one draw and one defeat from their six games.
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