The Imps held out for almost a half before Theo Walcott broke the deadlock, but Cowley insists it has been a ‘brilliant journey.’
The 38-year-old spoke at his post-match press conference before insisting he was ready to go and see Wenger ‘to learn some more.’
“He’s invited us in for a coke so we’ll go in there and try to learn some more,” Cowley said after the FA Cup quarter-final.
The Imps played nine matches to reach the quarter-finals of the competition which included four scalps of Oldham, Ipswich, Brighton and Burnley before finally coming unstuck at the Emirates Stadium.
Walcott scored in first-half stoppage-time to break Lincoln hearts before second-half strikes from Olivier Giroud, Alexis Sanchez, Aaron Ramsey and a Luke Waterfall own goal saw the Premier League side reach the last four at Wembley.
Cowley’s side also became the first non-league team to reach the last eight of the FA Cup since QPR in 1914 and the 38-year-old is delighted they have claimed their place in the history books.
Cowley told BT Sport 2: “They have world-class players and when they scored on the edge of half-time it was always going to be difficult because they got confident from there on in.
“They possessed the ball so well and you can’t help but be negative. It was really tough but listen, we are the first non-league team in over 100 years to get to the last eight of the FA Cup.
“We will never be happy when we lose but I think at some stage we need to be proud with what we have done.
“This is not the time for criticism, I think this is the time for us to be able to reflect on what we have done in the FA Cup – it’s been a brilliant journey and the key is to learn from this.
“We played against world-class players today and we will learn from this experience and come away as better footballers and better people.
“I think this is a great learning curve for us, it is a real test for us as people – it is our challenge now to go into our two FA Trophy games to find our levels.”