The Pilgrims were eventually beaten 3-1 by Alan Pardew's side, despite for long periods looking as if they could win the tie. However in the last ten minutes with the scores locked at 1-1 first Steve Sidwell and then Nicky Forster netted to give the Berkshire side a dramatic win, against the run of play.
Defiant in defeat, Thompson congratulated his side on an excellent performance.
"We were playing against a team who have big expectations for themselves and we did very well," said the Boston boss.
"They want to be fighting at the top of Division One like last season and we matched them in the second half and that is something we can be proud of.
The home side, who were playing their biggest game in twenty-five years, were left to rue missed chances. The trigger-happy Royals had Marcus Hahnemann to thank for keeping the score down at the other end.
Had the Pilgrims finished as well as Reading then it would be they and not the Royals in the hat for the second round draw.
"In the first half we had two great chances with Peter Duffield and Stuart Douglas and if we had put those away it could have been a different story," added Thompson.
"We put them on the back foot but didn't make it pay for us. I don't think 3-1 really reflects the nature of the game."
"The only real difference was that Reading did the business when it mattered. The higher up you go in the Football League the more likely teams are to take chances they are offered and Reading took theirs when they came."
Thompson will now turn his side's attentions to the league. Boston are hoping for a top half finish in Division Three this season following a relegation battle last term. Their campaign didn't get off to the best possible start last weekend, they drew 0-0 with Macclesfield.
The Lincolnshire side are at home to Huddersfield Town on Saturday. The game will prove a tough test for the Pilgrims top-half aspirations, the Terriers were a Division One side three years ago.
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