Lamela scored Tottenham's goal against the French principality side in the first-half, but they were unable to hold on as Stephan El Shaarawy nodded in a late equaliser.
Although the draw wasn't a bad result on paper, the fact that they led in the match for so long left Spurs feeling frustrated after the match.
Kane said on Twitter that he was disappointed Spurs weren't able to pick up all three points, but he also found the time to congratulate teammate Dele Alli on his call-up to the senior England squad.
Alli was a surprise inclusion in the Three Lions squad for their Euro 2016 qualifiers against Estonia and Lithuania, and Kane, who was also named in Roy Hodgson's ranks, was delighted for his club colleague.
Lamela's stance on the Monaco match was slightly less negative, with the winger already looking ahead to the weekend, when the Lilywhites take on Swansea City.
Returning to London, not bad result playing away, looking forward to the next game on sunday. #COYS— Erik Manuel Lamela (@Coco_Lamela) October 1, 2015
Tottenham's draw against Monaco means that they have taken four points from their opening two Europa League games, putting them in a strong position to qualify from their group.