diff --git a/lib/internal/http2/core.js b/lib/internal/http2/core.js
index b7a56850a308c8..f3b23a6ec4f830 100644
--- a/lib/internal/http2/core.js
+++ b/lib/internal/http2/core.js
@@ -2472,8 +2472,17 @@ function connectionListener(socket) {
       return httpConnectionListener.call(this, socket);
     }
     // Let event handler deal with the socket
-    if (!this.emit('unknownProtocol', socket))
-      socket.destroy();
+    debug(`Unknown protocol from ${socket.remoteAddress}:${socket.remotePort}`);
+    if (!this.emit('unknownProtocol', socket)) {
+      // We don't know what to do, so let's just tell the other side what's
+      // going on in a format that they *might* understand.
+      socket.end('HTTP/1.0 403 Forbidden\r\n' +
+                 'Content-Type: text/plain\r\n\r\n' +
+                 'Unknown ALPN Protocol, expected `h2` to be available.\n' +
+                 'If this is a HTTP request: The server was not ' +
+                 'configured with the `allowHTTP1` option or a ' +
+                 'listener for the `unknownProtocol` event.\n');
+    }
     return;
   }
 
diff --git a/test/parallel/test-http2-https-fallback.js b/test/parallel/test-http2-https-fallback.js
index 01b694e586dd49..5d9a7e17103e56 100644
--- a/test/parallel/test-http2-https-fallback.js
+++ b/test/parallel/test-http2-https-fallback.js
@@ -6,7 +6,7 @@ const fixtures = require('../common/fixtures');
 if (!common.hasCrypto)
   common.skip('missing crypto');
 
-const { strictEqual } = require('assert');
+const { strictEqual, ok } = require('assert');
 const { createSecureContext } = require('tls');
 const { createSecureServer, connect } = require('http2');
 const { get } = require('https');
@@ -131,10 +131,17 @@ function onSession(session) {
 
     // HTTP/1.1 client
     get(Object.assign(parse(origin), clientOptions), common.mustNotCall())
-      .on('error', common.mustCall(cleanup));
+      .on('error', common.mustCall(cleanup))
+      .end();
 
     // Incompatible ALPN TLS client
+    let text = '';
     tls(Object.assign({ port, ALPNProtocols: ['fake'] }, clientOptions))
-      .on('error', common.mustCall(cleanup));
+      .setEncoding('utf8')
+      .on('data', (chunk) => text += chunk)
+      .on('end', common.mustCall(() => {
+        ok(/Unknown ALPN Protocol, expected `h2` to be available/.test(text));
+        cleanup();
+      }));
   }));
 }