Despite leading at the break, Sarries slumped to a fifth loss in seven games as tries from Irish duo Sailosi Tagicakibau and Gonzalo Tiesi saw the Exiles take another giant stride towards play-off qualification with a 27-24 win.
"We didn't get a great start to the game but there's no doubt we've improved since last week," said Gaffney.
"Some people won't like to hear me saying that but there's no doubt we did.
"We know we've been disappointing in the last two weeks and that doesn't make a difference who you play. We've just got to live with our own performances.
"You can't fault the effort of the players but at times we weren't as smart as we should have been and the lead at half-time was pretty much against the run of play."
Saracens have now scored just eight tries in their last six games and, with Irish number 15 Peter Hewat in fine form with his boot, scoring 17 points, Ben Skirving and Kameli Ratuvou touchdowns were never going to be enough for the visitors.
Trailing 13-12 at the break, Irish staged a second-half comeback with former England international Mike Catt pulling the strings and Tagicakibau and Tiesi scoring tries.
Replacement Ratuvou set up a nervy finale as he went over for Sarries in the 74th minute but it proved too little too late for the out-of-form visitors as Jackson fluffed his late penalty.
London Irish coach Tony Booth hailed his side's second half comeback, saying: "We came in at half-time in a one point ball game and to be honest it was quite astounding.
"We had the majority of quality possession at that stage and it just seemed amazing that it was so close still.
"To be honest, it's probably through rose tinted glasses but if we had of lost that game it would have been a travesty."